Prove The Identities., 1.) Cos\Xb2 Theta 2013 Cot \Xb2 Theta = -Cos\Xb2 Theta Cot\Xb2 Theta, 2.) Sec^4 Theta 2013 Sec^2 Theta = Tan^4 Theta + Tan^2 Th

Prove the identities.

1.) cos² theta – cot ² theta = -cos² theta cot² theta

2.) sec^4 theta – sec^2 theta = tan^4 theta + tan^2 theta

 

Step-by-step explanation:

1.) cos² theta – cot ² theta = -cos² theta cot² theta

Trigonometric identity: cot theta = cos theta / sin theta

cos² theta - (cos² theta/sin² theta) = -cos² theta cot² theta

factor out cos² theta

cos² theta1 - (1/sin² theta) = -cos² theta cot² theta

Trigonometric identity: csc theta = 1/sin theta

cos² theta(1 - csc² theta) = -cos² theta cot² theta

Trigonometric identity: 1 - csc² theta = -cot² theta

-cos² theta cot² theta  = -cos² theta cot² theta

2.) sec^4 theta – sec^2 theta = tan^4 theta + tan^2 theta

sec^2 theta (sec^2 theta – 1) = tan^4 theta + tan^2 theta

Trigonometric identity: 1 + tan² theta = sec² theta

1 +tan² theta ( tan² theta ) = tan^4 theta + tan^2 theta

tan^4 theta + tan^2 theta = tan^4 theta + tan^2 theta