Question

if sinA=3/5then find the values of the following sin3A cos3A tan3A cot3A​

Answer 1

Answer:

sin3A = 9/5

cos3A = 12/5

tan3A = 3/4

cot3A = 4/3

Step-by-step explanation:

USE IMAGE OF TRIANGLE GIVEN BELOW AS REFERENCE

sin A = 3/5 = O/H

Let A = ∠B

So, 3/5 = O/H

Comapring, O = AC = 3 and H = AB = 5.

By Pythagoras' theorem, AB² = AC² + BC²

=> 5² = 3² + BC²

=> BC² = 5² - 3²

=> BC² = 25 - 9 => 16

∴ BC = √16 => 4 (units)

sinA = 3/5 (given)

So, sin3A = 3(3/5) => 9/5

cosA = P/H = 4/5

So, cos3A = 3(4/5) => 12/5

tan3A = sin3A/cos3A (As tanA = sin3A/cosA)

=> 9/5 ÷ 12/5

=> 9/5(5/12)       (Dividing by a number is the same as multiplying by its reciprocal)

=> (9/12)(5/5)

=> (9/12)*1 => 9/12 => 3/4 (Dividing by 3)

cot3A = 1/tan3A (As cotA = 1/tanA)

=> 1/(3/4)

=> 1 ÷ 3/4

=> 1(4/3) => 4/3          (Dividing by a number is the same as multiplying by its reciprocal)