Question

Solve it, if you have one father. Don't give sh*t answer​

Answer 1

Please refer to the attachment.

How did I solve?

1. We have a odd term which is tan x on the left hand side. So, we write it as sin x / cos x
2. Simplifying it a bit more, we observe that the denominators of the fractions are of opposite signs, so we take negative common.
3. Now the denominators are the same so, we add up the numerator directly while the denominator remains the same.
4. We get an expression of a³ - b³ which we can expand using the identity which is equal to (a - b)(a² + b² + ab)
5. Now cos x - sin x gets cancelled out so we are left with only sin²x + cos²x + sin x cos x
6. But, we know, sin² x + cos² x = 1, So the expression gets simplified to 1 + sin x cos x. That is what we needed to prove.

Other formulae :-

◉ 1 + tan² θ = sec² θ

◉ 1 + cot² θ = cosec² θ

• sin x = 1 / cosec x
• cos x = 1 / sec x
• tan x = 1 / cot x