Verify the identity - sinx-2-cosx

Verifying the trigonometric identity Given trigonometric expression is sin(x+π/2)=cosx.Taking L.H.S⇒sin(x+π/2)=sinx.cos(π/2)+cosx.sin(π/2) [∵sin(a+b)=sin(a ...

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Standard IX

Mathematics

Inverse of a Function

Verify the id...

Question

Verify the identity : $\sin (x + \frac{π}{2}) = \cos x$

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Solution

Verifying the trigonometric identity
Given trigonometric expression is $\sin (x + \frac{π}{2}) = \cos x$ .
Taking $L . H . S$
$\Rightarrow \sin (x + \frac{π}{2}) = \sin x . \cos (\frac{π}{2}) + \cos x . \sin (\frac{π}{2}) [∵ \sin (a + b)= \sin (a) \cos (b) + \cos (a) \sin (b)] = \sin x . 0 + \cos x . 1 [∵ \cos (\frac{π}{2}) = 0 and \sin (\frac{π}{2}) = 1]$
$= \cos x$
$=$ $L . H . S$
Hence proved.

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Verify the identity : sinx+π2=cosx

Verifying the trigonometric identity Given trigonometric expression is sinx+π2=cosx.Taking L.H.S⇒sinx+π2=sinx.cosπ2+cosx.sinπ2∵sin(a+b)=sinacosb+cosasinb=sinx.0+cosx.1[∵cos(π2)=0andsin(π2)=1]=cosx =L.H.SHence proved.

Verify the identity : $\sin (x + \frac{π}{2}) = \cos x$