Use a difference identity to prove than tan(0+ π) = tan(0).

Q: 1. 3 evaluate tan 2 x . 4 Given that tan x=-

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Q: 5. Simplify the expression: tan (csc (x)). Assume x is defined appropriately.

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Q: verify the identity tan(x/2) + cot(x/2) = 2 csc x

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Q: Verify the identity: sin x/(1 + cos x) = (1 - cos x)/sin x.

A: sinx1+cosx=sinx1+cosx×1-cosx1-cosx=sinx1-cosx1-cos2x     ∵a+ba-b=a2-b2=sinx1-cosxsin2x…

Q: Suppose that tan(x) = 2. Compute tan (x + 1).

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Q: Find the exact value of tan (-1), if it exists. Give convincing reasons for your answer.

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Q: Verify the identity: tan x + 1/tan x = 1/(sin x cos x)

A: To verify: tan x+1tan x=1sinx. cosx

Q: Assume a is positive, find cos(tan-) (show your work)

A: Given, x is positive To find cos(tan-1x)

Q: Verify that it is an identity  (1-sec/tan)+(tan/1-sec)=-2csc

A: We will simplify left side and make it equal to right side

Q: 1 2. - + tanx = tanx sinxcosx

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Q: Find the exact Value of -1 Cos (tan'a + Sin ¹ 1/27) 13

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Q: can you simplify sin(tan-1(x)) thanks

A: Step 1:To simplify sin(tan−1(x)) we can use a bit of trigonometric and algebraic manipulation.…