Question

if sin 10 theta is equal to cos 8 theta and 10 theta is a positive acute angle let us find the value of tan
9 thet
a​

Answer 1

Step-by-step explanation:

sin 10 theta = cos 8 theta

cos (90°- 10 theta)=cos 8 theta

90°-10 theta =8 theta

90° = 10 theta + 8 theta

90°=18 theta

theta = 90°/18

theta = 5°

Now,

tan 9 theta = tan 9×5

tan 45°= 1

ans: 1

Answer 2

The value of tan 9θ = 1.

Given :

sin 10 θ = cos 8 θ and 10 θ is acute

To find :

The value of tan 9θ.

Solution:

Given that sin 10 θ = cos 8 θ and 10 θ is acute.

sin 10 θ = sin (90 - 8θ)

10θ = 90 - 8θ

10θ + 8θ = 90

18θ = 90

θ = 90/18

θ = 5

9θ = 9 * 5 = 45.

Therefore,

tan 9θ = tan 45

tan 9θ = 1

Hence , the value of tan 9θ = 1.

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