Question #6abe5

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Question #6abe5

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Answer 1 · 2017-10-25T15:42:34

Start by writing the LHS as a single fraction, expand and simplify the denominator and then use c^2+s^2=1 to simplify it further.

Explanation:

LHS denominator becomes $(1 - sin θ) (1 + sin θ) = (1 - {sin}^{2} θ)$ $(1-sin theta)(1+sin theta)=(1-sin^2 theta)$ . Using the pythagorean identity, this is ${cos}^{2} θ$ $cos^2 theta$ .
The LHS numerator is ${(1 + sin θ)}^{2} - {(1 - sin θ)}^{2}$ $(1+sin theta)^2-(1-sin theta)^2$
$= (1 + sin θ + 1 - sin θ) (1 + sin θ - 1 + sin θ)$ $=(1+sin theta+1-sin theta)(1+sin theta-1+sin theta)$
$= 2 (2 sin θ)$ $=2(2sin theta)$
$= 4 sin θ$ $=4sin theta$
So LHS is now $\frac{4 sin θ}{{cos}^{2} θ} = 4 sin θ {sec}^{2} θ$ $(4sin theta)/cos^2 theta=4sin theta sec^2 theta$

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Question #6abe5

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