An equation like sin2 u + cos2 u = 1 is called an identity because it holds for all values of u. An equation like sin u = 0.5 is not an identity because it holds only for selected values of u, not all. If you differentiate both sides of a trigonometric identity in u with respect to u, the resulting new equation will also be an identity. Differentiate the following to show that the resulting equa-tions hold for all u. a. sin 2u = 2 sin u cos u b. cos 2u = cos2 u - sin2 u

Q: cos -1

A: Given: cos-122=θ22=cos θ12=cos θθ=π4cos-122=π4

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A: Some Trigonometric formula,                             1.   sin2θ+cos2θ=12.   sin2θ = 2sinθcosθ3.…

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A: We need to prove the following condition 1+sinθ1-sinθ = cos2θ

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A: Given

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A: Given: Since, So,

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A: Topic:- trigonometry

Q: 5. Is the equation cos 0 – sin 0 =1 an identity? If so, verify it. If not, explain why. %3D

A: The trigonometric equation is an identity if it is true for all cases. To check if the equation is…

Q: Verify the identity by transforming the lefthand side into the right-hand side.

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A: Given equation,

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A: To find : value of x for which cos(3x) = x if exists

Q: If 0 < α < π/2, and sin α = 1/3, evaluate the following in exact form.  a. sin α/2 b. cos 2α

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Q: verify the trigonometric identity below. 1+ sin(2θ)+(sin(θ)+cos(θ))^2

A: Given data 1+sin2θ=sinθ+cosθ2

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Q: If tan θ= (√2)/5 and π (greater than) θ (greater than) 3 π/2, find the exact value of cos 2 θ

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Q: Use the facts that cos (π/6)=((√3)/2) and sin (π/6)=1/2 to find the exact value of tan ( π/12)

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A: Explanation of the answer is as follows

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Q: 5. Is the equation cos 0 - sin 0 = 1 an identity? If so, verify it. If not, explain why. %3D

A: As we know that an identity is satisfied by any value of variable . Let's check for given equation .

Q: 1. Determine an exact value for the following expression: л sin COS sec+tan 444 4

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Q: If tan 0 = V3 and 0 < 0 < <o< 플 then, Select one: O sin0 = - 10 O sin 0 = - cos 0 = cos e

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Q: If cos (0) = - and tan (0) < 0, find all other trigonometric functions of 0.

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.