Question

The value of sin²41 + cos²49 will be ​

Answer 1

Appropriate Question :-

Find value of $\sf \sin² 41° + \sin² 49°$

Given :-

$\quad \leadsto \quad \sf \sin² 41° + \sin² 49°$

To Find :-

Value of the above expression

Solution :-

Before starting the answer , let's recall that ;

• $\sf \sin ( 90 - \theta ) = \cos \theta$

• $\sf \sin² \theta + \cos² \theta = 1$

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Consider given ;

$\quad \leadsto \quad \sf \sin² 41° + \sin² 49°$

Can be written as ;

${ : \implies \quad \sf \{ \sin ( 41° )\}² + \sin² 49°}$

Can further written as ;

${ : \implies \quad \sf \{ \sin ( 90 - 49 )\}² + \sin² 49°}$

Can again written as using the 1st identity ;

${ : \implies \quad \sf \{ \cos ( 49°) \}² + \sin² 49°}$

${ : \implies \quad \sf \cos² 49°+ \sin² 49°}$

Using above identity 2 ;

${ : \implies \quad \bf \therefore \quad \underline{ \underline {1 }}}$

Henceforth , The Required Answer is 1 :)