Question

tan 3 tan 63 tan 57=cot A find A

Answer 1

Tan3*tan63*tan57=cot87*cot27*cot33 =cot(87+27+33)=cot147

Answer 2

A = 81°

Step-by-step explanation:

Given,

tan3° tan63° tan57° = cotA

or, tan3° tan(60° + 3°) tan(60° - 3°) = cotA

or, tan3° {(tan²60° - tan²3°)/(1 - tan²60° tan²3°)} = cotA

or, tan3° {(3 - tan²3°)/(1 - 3 tan²3°)} = cotA

or, (3 tan3° - tan³3°)/(1 - 3 tan²3°) = cotA

or, tan(3 × 3°) = cotA

or, tan9° = cotA

or, tan(90° - 81°) = cotA

or, cot81° = cotA

or, A = 81°

Therefore A = 81°

Trigonometric formulae:

1. tan(90° - θ) = cotθ

2. tan3θ = (3 tanθ - tan³θ)/(1 - 3 tan²θ)

Try these problems at home:

1. Prove that, tan20° tan40° tan80° = √3

2. If A + B = 225°, then show that, cotA/(1 + cotA) . cotB/(1 + cotB) = 1/2

3. If cosx/cosy = a/b, then show that, a tanx + b tany = (a + b) tan{(x + y)/2}