Question

Without using trigonometrical tables, evaluate:

5 cos 0° - 2 sin 30° + √3 cos 30°
__________________________+ 3 sin
29° sec 61°
tan 30° x tan 60° x cos 60°
pls answer fast.....​

Answer 1

value of given expression is 14.

we have to find value of (5cos0° - 2sin30° + √3cos30°)/(tan30° × tan60° × cos60°) + 3sin29°. sec61°

we know, cos0° = 1, sin30° = 1/2 , cos30° = √3/2

so, (5 × 1 - 2 × 1/2 + √3 × √3/2)/{(tan30° × tan(90° - 30°) × cos60°} + 3sin29°. sec(90° - 29°)

we know, tan(90° - θ) = cotθ

and sec(90° - θ) = cosecθ

= (5 - 1 + 3/2)/(tan30°. cot30°. cos60°) + 3sin29°. cosec29°

we also know, tanθcotθ = 1

and sinθcosecθ = 1

and cos60° = 1/2

= (11/2)/( 1 × cos60°) + 3 × 1

= (11/2)/(1/2) + 3

= 11 + 3

= 14