Question

show that cos÷1+sin=1-sin÷cos​

Answer 1

Answer:

cosx+cosx1−sinx=2secx Proved.

Step-by-step explanation:

Consider the provided equation.

\frac{\cos x}{1-\sin x} +\frac{1-\sin x}{\cos x} =2\sec x1−sinxcosx+cosx1−sinx=2secx

Consider the LHS.

\frac{\cos x}{1-\sin x} +\frac{1-\sin x}{\cos x}1−sinxcosx+cosx1−sinx

\frac{\cos^2 x+(1-\sin x)^2}{\cos x(1-\sin x)}cosx(1−sinx)cos2x+(1−sinx)2

\frac{\cos^2 x+1+\sin^2 x-2\sin x}{\cos x(1-\sin x)}cosx(1−sinx)cos2x+1+sin2x−2sinx

Use the identity sin²x+cos²x=1

\frac{1+1-2\sin x}{\cos x(1-\sin x)}cosx(1−sinx)1+1−2sinx

\frac{2-2\sin x}{\cos x(1-\sin x)}cosx(1−sinx)2−2sinx

\frac{2(1-\sin x)}{\cos x(1-\sin x)}cosx(1−sinx)2(1−sinx)

\frac{2}{\cos x}cosx2

2\sec x2secx

LHS=RHS

Hence, proved

#Learn more

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

https://brainly.in/question/3856518

Answer 2

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