Question

Evaluate : 2 x sin68 x sec22 / sec2(90-theta) - cot2theta + sin264 + cos64 x sin 26 / sec45 x cosec45 x cos60

Answer 1

Sin² A + Cos² A = 1
Cosec² A - Cot² A = 1
Sec 22° = Cosec (90° - 22°) = Cosec 68°
Sin 26° = Cos (90° - 26°) = Cos 64°
Cos60 = Sin 30 = 1/2
Cosec 45° = 1/sin45° = √2
Sec 45° = 1/cos45° = √2

$\frac{2 \times Sin68^o \times Sec 22^o}{Sec^2(90^o-\theta)-cot^2\theta}+\frac{Sin^2 64^o+cos64^o \times Sin26^o}{Sec45^o \times Cosec45^o \times Cos60^o}\\\\=\frac{2 Sin 68^o \times cosec68^o}{Cosec^2\theta-cot^2\theta}+\frac{Sin^2 64^o+cos^2 64^o}{\sqrt2 \times \sqrt2 \times \frac{1}{2}}\\\\=2 +1=3$