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 tan9theta​

Answer 1

Answer:

Here is your answer ✌️

sin 10 theta = cos 8 theta

therefore, sin 10 theta = sin ( 90° - 8 theta )

Comparing both sides ,

=> 10 theta = 90° - 8 theta

=> 18 theta = 90°

=> theta = 90°/18

=> theta = 5°

therefore, 9 theta = 9 × 5

= 45°

therefore, value of tan 9 theta = tan 45°

= 1 [ Since tan 45° = 1 ]

Step-by-step explanation:

Hope it helps you ....

Answer 2

Question:-

• If $\sin 10\theta=\cos8\theta$ and $\theta$ is a positive acute angle, find the value of $\tan 9\theta$

Solution:-

According to the question,

$\sin10 \theta = \cos8 \theta$

Now, using the complementary angle formula, we can write like this,

$\sin10 \theta = \cos(90 \degree- (90 \degree- 8 \theta) )$

$\implies \sin10 \theta = \sin(90 \degree - 8 \theta)$

$\implies 10 \theta =90 \degree - 8 \theta$

$\implies (10 + 8) \theta = 90 \degree$

$\implies 18 \theta = 90 \degree$

$\implies \theta = \frac{90}{18} \degree$

$\implies \theta = 5 \degree$

Therefore,

$\tan9 \theta = \tan45 \degree$

$= 1$

Since, $\tan45\degree=1$.

Answer:-

$\tan9 \theta = \tan45 \degree = 1$