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Proofs using Trigonometric Identities

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Proofs using Trigonometric Identities

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Practice: Proofs using Trigonometric Identities

True or False?

(sin⁡θ−cos⁡θ)2+(sin⁡θ+cos⁡θ)2=2(\sin\theta-\cos\theta)^2+(\sin\theta+\cos\theta)^2=2.
More Proofs using Trigonometric Identities Questions:
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
Which of the following is equivalent to tan⁡2θ+1+tan⁡θsec⁡θ\tan^2\theta+1+\tan\theta\sec\theta?
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
Which of the following is equivalent to sin⁡2θ+4sin⁡θ+3cos⁡2θ\dfrac{\sin^2\theta+4\sin\theta+3}{\cos^2\theta}?
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
True or False?
cos⁡2θ=csc⁡θcos⁡θtan⁡θ+cot⁡θ\cos^2\theta=\dfrac{\csc\theta\cos\theta}{\tan\theta+\cot\theta}.
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
True or False?
1tan⁡θ+tan⁡θ=sin⁡θcos⁡θ\dfrac{1}{\tan\theta}+\tan\theta=\sin\theta\cos\theta
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
True or False?
tan⁡θsin⁡θ+cos⁡θ=sec⁡θ\tan\theta\sin\theta+\cos\theta=\sec\theta
Double & Half Angle Identities
Practice: Double & Half Angle Identities
True or False? csc⁡2θ−2csc⁡2θ=sin⁡2θ\dfrac{\csc^2\theta-2}{\csc^2\theta}=\sin2\theta
Double & Half Angle Identities
Practice: Double & Half Angle Identities
True or False? sin⁡2θ1−cos⁡2θ=2csc⁡2θ−tan⁡θ\dfrac{\sin2\theta}{1-\cos2\theta}=2\csc2\theta-\tan\theta
Reciprocal & Quotient Identities
Practice: Reciprocal & Quotient Identities
Simplify cot⁡θ+12cos⁡θ\cot\theta+\dfrac{1}{2}\cos\theta.
Reciprocal & Quotient Identities
Practice: Reciprocal & Quotient Identities
True or false: tan⁡θcsc⁡2θsec⁡θ=sec⁡θ\dfrac{\tan\theta\csc^{2}\theta}{\sec\theta}=\sec\theta.
Reciprocal & Quotient Identities
Practice: Reciprocal & Quotient Identities
True or false: cot⁡2θsin⁡θcsc⁡θ=cos⁡2θ\dfrac{\cot^2\theta\sin\theta}{\csc\theta}=\cos^2\theta.
More Proofs using Trigonometric Identities Questions:
Trigonometric Identities & Proofs
True or false:
1+sin⁡x1−sin⁡x−1−sin⁡x1+sin⁡x=4tan⁡xcsc⁡x\dfrac{1+\sin{x}}{1-\sin{x}}-\dfrac{1-\sin{x}}{1+\sin{x}}=4\tan{x}\csc{x}
Trigonometric Identities & Proofs
Determine an equivalent expression to 1+cos⁡xsin⁡x\dfrac{1+\cos{x}}{\sin{x}}.
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
Which of the following is equivalent to tan⁡2θ+1+tan⁡θsec⁡θ\tan^2\theta+1+\tan\theta\sec\theta?
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
Which of the following is equivalent to sin⁡2θ+4sin⁡θ+3cos⁡2θ\dfrac{\sin^2\theta+4\sin\theta+3}{\cos^2\theta}?
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
True or False?
cos⁡2θ=csc⁡θcos⁡θtan⁡θ+cot⁡θ\cos^2\theta=\dfrac{\csc\theta\cos\theta}{\tan\theta+\cot\theta}.
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
True or False?
1tan⁡θ+tan⁡θ=sin⁡θcos⁡θ\dfrac{1}{\tan\theta}+\tan\theta=\sin\theta\cos\theta
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
True or False?
tan⁡θsin⁡θ+cos⁡θ=sec⁡θ\tan\theta\sin\theta+\cos\theta=\sec\theta
Double & Half Angle Identities
Practice: Double & Half Angle Identities
True or False? csc⁡2θ−2csc⁡2θ=sin⁡2θ\dfrac{\csc^2\theta-2}{\csc^2\theta}=\sin2\theta
Double & Half Angle Identities
Practice: Double & Half Angle Identities
True or False? sin⁡2θ1−cos⁡2θ=2csc⁡2θ−tan⁡θ\dfrac{\sin2\theta}{1-\cos2\theta}=2\csc2\theta-\tan\theta
Reciprocal & Quotient Identities
Practice: Reciprocal & Quotient Identities
Simplify cot⁡θ+12cos⁡θ\cot\theta+\dfrac{1}{2}\cos\theta.
Reciprocal & Quotient Identities
Practice: Reciprocal & Quotient Identities
True or false: tan⁡θcsc⁡2θsec⁡θ=sec⁡θ\dfrac{\tan\theta\csc^{2}\theta}{\sec\theta}=\sec\theta.
Reciprocal & Quotient Identities
Practice: Reciprocal & Quotient Identities
True or false: cot⁡2θsin⁡θcsc⁡θ=cos⁡2θ\dfrac{\cot^2\theta\sin\theta}{\csc\theta}=\cos^2\theta.
More Proofs using Trigonometric Identities Questions:
Trigonometric Identities & Proofs
True or false:
1+sin⁡x1−sin⁡x−1−sin⁡x1+sin⁡x=4tan⁡xcsc⁡x\dfrac{1+\sin{x}}{1-\sin{x}}-\dfrac{1-\sin{x}}{1+\sin{x}}=4\tan{x}\csc{x}
Trigonometric Identities & Proofs
Determine an equivalent expression to 1+cos⁡xsin⁡x\dfrac{1+\cos{x}}{\sin{x}}.
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
Which of the following is equivalent to tan⁡2θ+1+tan⁡θsec⁡θ\tan^2\theta+1+\tan\theta\sec\theta?
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
Which of the following is equivalent to sin⁡2θ+4sin⁡θ+3cos⁡2θ\dfrac{\sin^2\theta+4\sin\theta+3}{\cos^2\theta}?
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
True or False?
cos⁡2θ=csc⁡θcos⁡θtan⁡θ+cot⁡θ\cos^2\theta=\dfrac{\csc\theta\cos\theta}{\tan\theta+\cot\theta}.
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
True or False?
1tan⁡θ+tan⁡θ=sin⁡θcos⁡θ\dfrac{1}{\tan\theta}+\tan\theta=\sin\theta\cos\theta
Proofs using Trigonometric Identities
Practice: Proofs using Trigonometric Identities
True or False?
tan⁡θsin⁡θ+cos⁡θ=sec⁡θ\tan\theta\sin\theta+\cos\theta=\sec\theta
Double & Half Angle Identities
Practice: Double & Half Angle Identities
True or False? csc⁡2θ−2csc⁡2θ=sin⁡2θ\dfrac{\csc^2\theta-2}{\csc^2\theta}=\sin2\theta
Double & Half Angle Identities
Practice: Double & Half Angle Identities
True or False? sin⁡2θ1−cos⁡2θ=2csc⁡2θ−tan⁡θ\dfrac{\sin2\theta}{1-\cos2\theta}=2\csc2\theta-\tan\theta
Reciprocal & Quotient Identities
Practice: Reciprocal & Quotient Identities
Simplify cot⁡θ+12cos⁡θ\cot\theta+\dfrac{1}{2}\cos\theta.
Reciprocal & Quotient Identities
Practice: Reciprocal & Quotient Identities
True or false: tan⁡θcsc⁡2θsec⁡θ=sec⁡θ\dfrac{\tan\theta\csc^{2}\theta}{\sec\theta}=\sec\theta.
Reciprocal & Quotient Identities
Practice: Reciprocal & Quotient Identities
True or false: cot⁡2θsin⁡θcsc⁡θ=cos⁡2θ\dfrac{\cot^2\theta\sin\theta}{\csc\theta}=\cos^2\theta.