The value of $\frac{\left(\cos 9^{\circ}+\sin 81^{\circ}\right)\left(\sec 9^{\circ}+{cosec} 81^{\circ}\right)}{2 \sin ^2 63^{\circ}+1+2 \sin ^2 27^{\circ}}$ is:
Answer & explanation
Correct answer: option 2
By using concept :-
sinA = ccosB Iff A + B = 90º
sinA = \(\frac{1}{cosecA}\)
secA = \(\frac{1}{cosA}\)
sin²A + cos²A = 1
Now,
\(\frac{(cos9º+sin81º).(sec9º+cosec81º)}{2sin²63º + 1 + 2 sin²27º}\)
= \(\frac{ cos9º.sec9º + cos9º.cosec81º + sin81º.sec9º+ sin81º.cosec81º}{2sin²63º + 1 + 2 cos²63º}\)
= \(\frac{ 1 + sin81º.cosec81º + cos9º.sec9º+1}{2 + 1 }\)
= \(\frac{ 1 + 1 +1+1}{2 + 1 }\)
= \(\frac{4}{3 }\)