Question

(1 + 10 square theta bracket close cos theta into sin theta is equal to 10 theta​

Answer 1

Answer:

$(1 + {tan}^{2} \alpha ). \cos( \alpha ) . \sin( \alpha ) = \tan( \alpha ) \\ we \: know \: that \\ 1 + {tan}^{2} \alpha = {sec}^{2} \alpha \\ now \: on \: taking \: left \: hand \: side \\ {sec}^{2} \alpha . \cos( \alpha ) . \sin( \alpha ) \\ = \frac{1}{ {cos}^{2} \alpha } . \cos( \alpha ). \sin( \alpha ) \\ = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \\ = \tan( \alpha ) \\ = right \: hand \: side \\ \: \: \: \: \: \: \: \: \: \: \: hence \: proved$

I hope it will help you ☺☺