Question

Find one by sin 10 degrees minus root 3 by cos 10 degrees is equals to

Answer 1

Ques. 1/sin10° - √3/cos10°
Answer: 4
Solution:
Multiply Both Numerator and Denominator by (sin10° × cos10°).

And Multiply Both Numerator & Denominator by 2.

We get:

2(1/2cos10° - √3/2sin10°)/(sin10° cos10°) ___(i)

Now as you know, sin30° = cos60° = 1/2

And, sin 60° = cos30° = √3/2

(i) →

2(sin30° cos10° - cos30° sin 10°)/(sin10° cos10°)

→ 2sin(30°-10°)/(sin10° cos10°)

→ 2 sin20° /(sin10° cos10°)

→ 2(2 sin10° cos10°)/(sin10° cos10°)

→ 4

or

You can choose to do:

2(cos60° cos10° - sin60° sin 10°)/(sin10° cos10°)

→ 2 cos(60° + 10°)/(sin10° cos10°)

→ 2 cos70°/(sin10° cos10°)

Thankyou!!!