Question

Write the value of cot square threta - 1 upon sin square threta

Answer 1

Answer:

Numerical value of the given equation is - 1 .

Step-by-step explanation:

Solution of this equation is given by two method, methods are given below :-

                      Method 1

= >  cot^2 θ - 1 / sin^2 θ

= >  cot^2 θ- cosec^2 θ

from the identities of trigonometry, we know that the value of cot^2 A is cosec^2 A - 1 .

= >  ( cosec^2 θ - 1 ) - cosec^2 θ

= >  cosec^2 θ - 1 - cosec^2 θ

= >  cosec^2 θ - cosec^2 θ - 1

= >  - 1

               Method 2

= >  cot^2 θ - 1 / sin^2 θ

= >  cos^2 θ / sin^2 θ - 1 / sin^2 θ

= >  ( 1 / sin^2 θ ) [ cos^2 θ - 1 ]

= >  - 1 / sin^2 θ x ( 1 - cos^2 θ )

From the identities of trigonometry we know that the value of 1 - cos^2 A is sin^2 A.

= >  - 1 / sin^2 θ x sin^2 θ

= >  - 1 x 1

= >  - 1