Prove that: (tanΘ + cotΘ)² = (1 + tan²Θ) + (1 + cot²Θ) 

Answer:


Before solving this question,
Let us understand

(a+b)² = a² + 2ab + b²

tanΘ * cotΘ = 1

Now solving the question we have,
(TanΘ + cotΘ)² when tanΘ = a and cotΘ = b

We have,
a² + 2ab + b² = tan²Θ + 2 tanΘ cotΘ + cot²Θ

Since tanΘ*cotΘ = 1

We get

Tan²Θ + 2 * 1 + cot²Θ
When we expand 2 as 1 + 1

We get
Tan²Θ +1 + 1+ cot²Θ which is equal to the RHS.

Therefore, you solve this type of trigonometric identity questions in the above-mentioned way in Trigonometry.

#SciPiTutor
#TrigonometricIdentities
#Trigonometry
#Mathematics