Question

Plz solve this sum. it's of class 10. chapter trigonometry.

Answer 1

According to given sum,

$lhs = {( \tan(a) + \csc(b) )}^{2} - {( \cot(b) - \sec(a) ) }^{2}$

${( \tan(a) )}^{2} + { \csc(b) }^{2} + 2 \tan(a) \csc(b) - ( { \cot(b) }^{2} { \sec(a) }^{2} + 2 \cot(b) \sec(a)$

${ \tan(a) }^{2} - { \sec(a) }^{2} + { \csc(b) }^{2} - { \cot(b) }^{2} + 2 \tan(a) \csc(b) + 2 \cot(b) \sec(a)$

$- 1 + 1 + 2 \tan(a) \csc(b) + 2 \cot(b) \sec(a)$

$2 \tan(a) \csc(b) + 2 \cot(b) \sec(a)$

$2 \tan(a) \cot(b) ( \frac{ \csc(b) }{ \cot(b) } + \frac{ \sec(a) }{ \tan(a) }$

$2 \tan(a) \cot(b) ( \sec(b) + \csc(a) )$

Here, LHS=RHS

hence proved.


:-)Hope it helps u.