Question

1 by 1-sin(alpha)+1by1+sin(alpha)=2sec²(alpha) proove​

Answer 1

Answer:

the proof is given in the image

Step-by-step explanation:

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Answer 2

Proving:

Step-by-step explanation:

$\ Given \ value: \\\\\frac{1}{1-\sin\alpha}+\frac{1}{1+\sin\alpha} = 2 \sec^2 \alpha\\\\\ Solution:\\\\\ Solve \ L.H.S \ part: \\\\\rightarrow \frac{1}{(1-\sin\alpha)}+\frac{1}{(1+\sin\alpha)} \\\\\rightarrow \frac{(1+\sin\alpha)+(1-\sin\alpha)}{(1-\sin\alpha)(1+\sin\alpha)} \\\\\rightarrow \frac{1+\sin\alpha+1-\sin\alpha}{(1-\sin\alpha)(1+\sin\alpha)} \\\\\rightarrow \frac{1+1}{(1-\sin\alpha)(1+\sin\alpha)} \\\\\rightarrow \frac{2}{(1-\sin\alpha)(1+\sin\alpha)} \\\\\ formula:\\\\ a^2-b^2 = (a+b)(a-b)$

$\rightarrow \frac{2}{((1)^2-\sin^2\alpha)} \\\\\therefore 1-\sin^2\alpha = \cos^2\alpha \\\\\rightarrow \frac{2}{(\cos^2\alpha)} \\\\\ \frac{1}{cos} \ = sec \\\\\rightarrow 2\sec^2\alpha$

$\ L.H.S\ = \ R.H.S$

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• Proving: https://brainly.in/question/3503668