Question

find tan 3A, if sin 3A=cos45°​

Answer 1

Given: sin 3A = cos 45°.

To find: The value of tan 3A.

Answer:

It's given that sin 3A = cos 45°.

Sine and cosine are equal at an angle of 45°.

[sin 45° = cos 45° = 1/√2]

⇒ 3A = 45

A = 45/3

A = 15°

We now have the value of A. Using it to find tan 3A,

⇒ tan 3*15°

= tan 45°

= 1

Answer 2

SOLUTION

• The value of tan3A for A = 45° is - 1

Given

$\sf \: \sin3A = \cos(45)$

To finD

Value of tan3A

We know that,

• sin∅ = cos(90 - ∅)

Implies,

$\longrightarrow \: \sf \: cos(90 - 3A) = cos45 \\ \\ \longrightarrow \: \sf \: 90 - 3A = 45 \\ \\ \longrightarrow \: \sf \: 3A = 135 \\ \\ \longrightarrow \ \boxed { \boxed{\sf \: A = 45}}$

Now,

$\sf \: tan3x \\ \\ \dashrightarrow \: \sf \: tan3(45) \\ \\ \dashrightarrow \: \sf \: tan135 \\ \\ \dashrightarrow \sf tan(90 + 45)$

NoTE

• (90 + ∅) lies in second quadrant and only sine and cosecant functions are positive

• tan(90 + ∅) = cot∅

Thus,

$\dashrightarrow \: \sf \: - \: cot45 \\ \\ \dashrightarrow \: - 1$