Question

show that cos/1-sin+1-sin/cos=2sec

Answer 1

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Answer 2

$\frac{\cos x}{1-\sin x} +\frac{1-\sin x}{\cos x} =2\sec x$ Proved.

Step-by-step explanation:

Consider the provided equation.

$\frac{\cos x}{1-\sin x} +\frac{1-\sin x}{\cos x} =2\sec x$

Consider the LHS.

$\frac{\cos x}{1-\sin x} +\frac{1-\sin x}{\cos x}$

$\frac{\cos^2 x+(1-\sin x)^2}{\cos x(1-\sin x)}$

$\frac{\cos^2 x+1+\sin^2 x-2\sin x}{\cos x(1-\sin x)}$

Use the identity sin²x+cos²x=1

$\frac{1+1-2\sin x}{\cos x(1-\sin x)}$

$\frac{2-2\sin x}{\cos x(1-\sin x)}$

$\frac{2(1-\sin x)}{\cos x(1-\sin x)}$

$\frac{2}{\cos x}$

$2\sec x$

LHS=RHS

Hence, proved

#Learn more

Cos a /1 +sin a +1+sin a/cos a = 2 sec a

https://brainly.in/question/3856518