Prove that- 1-sin- -cos-21-sin- -cos-2-1-cos-1-cos-

(1+ sinθ cos θ )^2/(1+ sin θ +cos θ )^2=1 cos θ/1+ cos θ solving LHS we get ⇒ (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca ⇒1+sin^2θ +cos^2θ +2 sin θ 2 s ...

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Trigonometric Ratios Using Right Angled Triangle

Prove that: ...

Question

Prove that:
(1+sinθ−cosθ)²/(1+sinθ+cosθ)²=(1−cosθ)/(1+cosθ)

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\frac{1 - cos θ}{1 + cos θ} = {(\frac{sin θ}{1 + cos θ})}^{2}

Prove the following trigonometric identities:

Prove that:

(i) $\sqrt{\frac{s e c θ - 1}{s e c θ + 1}} + \sqrt{\frac{s e c θ + 1}{s e c θ - 1}} = 2 c o s e c θ$

(ii) $\sqrt{\frac{1 + s i n θ}{1 - s i n θ}} + \sqrt{\frac{1 - s i n θ}{1 + s i n θ}} = 2 c o s e c θ$

(iii) $\sqrt{\frac{1 + c o s θ}{1 - c o s θ}} + \sqrt{\frac{1 - c o s θ}{1 + c o s θ}} = 2 c o s e c θ$

(iv) $\frac{s e c θ - 1}{s e c θ + 1} = {(\frac{s i n θ}{1 + c o s θ})}^{2}$

\frac{sec θ - 1}{sec θ + 1} = {(\frac{sin θ}{1 + cos θ})}^{2}

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