Use the fundamental identities to fully simplify the express

Use the fundamental identities to fully simplify the expression. 1 - sin^2 (x)/cot^2 (x) + 2 cos^2 (x) In the first term of the given expression, make an appropriate trigonometric and cos(x). What other trigonometric identities are needed to rewrite the expression

Solution

{ ( 1 - sin^2 x ) / cot^2 x } + 2 cos^2 x

1 -sin^2 x = cos^2 x

cot^2 x = cos^2 x / sin^2 x

plugging the values in the expression

cos^2 x / cos^2x / sin^2 x + 2 cos^2 x

= sin^2 x + 2 cos^2 x

sin^2 x + cos^2 x + cos^2 x ( since sin^2 x + cos^2 x = 1)

the expression becomes

1 + cos^2 x