Question

Without using tables, evaluate :

 4 tan 60° sec 30°+ (sin 31° sec 59° + cot 59° cot 31°) ÷ (8 sin² 30°–tan² 45°)

Answer 1

4tan60∘⋅sec30 ∘+sin31∘⋅sec59∘ +cot59 ∘ ⋅cot31∘ −8⋅sin²30°−tan²45∘

=4⋅3⋅32+sin31∘⋅cos59∘1+sin59∘cos59∘⋅sin31∘cos31° −8⋅( 21) 2−(1) 2

Since,

=value of tan60. tan60°=√3,sec30=2/√3,sin30=1/2and 45=1)

=8+sin31/sin(90-59)+cos59/cos(90-59)×cos31/=cos(90-31)-8/4-1

Since,

=Sin θ=cos(90-θ) and cosθ=sin(90-θ)

=8+sin31/sin31+ cos59/cos31+cos59-2-1

=8+1+1-2-1

=7