Question

(viii) (sin A+ cosec A)2 + (cos A + sec A)2
=7+tan? A+ cot? A CBSE 2014, 12, 11, 10​

Answer 1

Step-by-step explanation:

$lhs = {( \sin( \alpha ) + \csc( \alpha )) }^{2} + {( \cos( \alpha ) + \sec( \alpha )) }^{2} \\ = {(\sin( \alpha )) }^{2} + {( \csc( \alpha )) }^{2} + { (\cos( \alpha )) }^{2} + {(\sec( \alpha )) }^{2} + 2 + 2$

$= 1 + 1 + {( \tan( \alpha )) }^{2} + 1 + {( \cot( \alpha )) }^{2} + 4 \\ = 7 + {( \tan( \alpha )) }^{2} + {( \cot( \alpha )) }^{2} \\ = rhs$

Hence proved.