(1 point) Get help entering answers Establish the identity: 1 sint Use your work

Question

(1 point) Get help entering answers Establish the identity: 1 sint Use your work to determine which of the following shows the correct steps in establishing the identity Choice A: cos t 1 sin t 1 sin t 1sin t (1- sinr)(1 sin t) 1+ sin t 1-(1 + sin t) = Sin t Choice B: cos t 1 sint 1- sin t 1sin t (1- sin(1 +sinr) 1 +sin t 1- (1 - sin t) Choice C: cos r 1 sin 1 sin t 1 +sin t (1 - sin) (1 +sin t) 1 + sin t - 1- (1+sin t) sin 1 Choice D: cos T 1 sin 1 +sin t (1 - sin ) (1 sin r) 1 +sin t - 1-(1 - sin t) sint

Explanation / Answer

Given

1 - (cos^2(t)/(1+sin t))

sin^2 t + cos^2 t = 1

cos^2 t = 1 - sin^2 t

1 - ((1-sin^2 t)/(1+sint))

1 - ((1-sin t)(1+sint)/(1+sin t)) ( a^2 - b^2 = (a-b)(a+b) )

cancels away (1+ sin t)

leaving 1 - (1 - sin t)

1-1+sin t

= sint

option B

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