Question

prove the above given trigonometric identity​

Answer 1

Step-by-step explanation:

Simplify cosecA and cotA as cosA and sinA. After that use the three hypotenuse - Side identities.

Answer 2

Step-by-step explanation:

To prove---->

Cot²A Cosec²B - Cot²B Cosec²B = Cot²A - Cot²B

Proof--->

LHS = Cot²A Cosec²B - Cot²B Cosec²A

We know that , 1 + cot²θ = Cosec²θ , applying it here , we get,

= Cot²A ( 1 + Cot²B ) - Cot²B ( 1 + Cot²A )

= Cot²A + Cot²A Cot²B - Cot²B - Cot²Α Cot²B

= Cot²Α - Cot² B = RHS

Additional information--->

1) Sin²θ + Cos²θ = 1

2) 1 + Cot²θ = Cosec²θ

3) 1 + tan²θ = Sec²θ

4) Sin ( 90° - θ ) = Cosθ

5) Cos ( 90° - θ ) = Sinθ

6) tan ( 90° - θ ) = Cotθ

7) Cot ( 90° - θ ) = tanθ

8) Sec ( 90° - θ ) = Cosecθ

9) Cosec( 90° - θ ) = Secθ