Question

Calculate the value of A, if: (tanA-1) (cosec3A-1)=0

Answer 1

Answer:

(tanA-1) (cosec3A-1) = 0

tanA-1 =0/ cosec3A-1

tanA-1 = 0

tanA= 1

tanA= tan 45°

A = 45°

Answer 2

Given:

$\sf\bullet ( \tan A - 1)( \cosec 3A - 1) = 0$

Find:

$\sf\bullet \: calculate \: value \: of \: A$

Solution:

Here,

$\sf ( \tan A - 1)( \cosec 3A - 1) = 0$

$\sf Either, \tan A - 1 = 0 \: or \: \cosec 3A - 1 = 0 \\ \\ \sf \tan A - 1 = 0 \\ \\ \sf \tan A = 1$

$\sf \implies \tan A = \tan {45}^{ \circ} \\ \\ \sf \therefore A = {45}^{ \circ}$

$\sf \implies \cosec 3A - 1 = 0 \\ \\ \implies \sf \cosec 3A = 1\\ \\ \sf \implies \cosec 3A = \cosec{90}^{ \circ}$

$\sf 3A = {90}^{ \circ} \\ \\ \sf A = {30}^{ \circ}$

Hence, A = 45°, 30°