Question

explain me the following identities
1. sin^2 theta + cos^2 theta=1
2. 1+tan^2 theta = sec^2 theta
3. 1+ cot^2 theta = cosec^2 theta​

Answer 1

Identities are kind of fixed formulas which will always be true.

The given identities of trigonometry are applicable only when Ø is less than 90° and more than 0° .

The meaning of these identities is that when we apply the value of Ø, the resultson both sides will be equal.

For example, let is see Ø as 45° .

1) Sin²∅ + cos²∅ =1

sin² 45 + cos²45 =1

(1/√2) ² +(1/√2)² =1

1/2 + 1/2 =1

1= 1

______________________

2) 1+ tan²∅ = sec² ∅

1+ tan²45 = sec²45

1+ (1)² = (√2)²

1+1 =2

2=2

_____________________

3) 1+ cot² ∅ = cosec²∅

1+ cot²45 = cosec²45

1+ (1)² = (√2)²

1+1 =2

2=2

_________________[HENCE VERIFIED]