Question

Verify the trig identity: tan^2 theta + cot^2 theta / csc^2 theta = sec^2 theta

Answer 1

Answer:

See proof below

Step-by-step explanation:

In trigonometry identity

tan^2 theta = sin^2 theta /cos^2 theta

cot^2 theta = cos^2 theta/sin^2 theta

csc^2 theta = 1/sin^2 theta

Substitute into the expression

(sin^2 theta /cos^2 theta )+ (cos^2 theta/sin^2 theta)/1/sin^2 theta

= [sin^4theta + cos^4theta/cos^2 theta sin^2 theta]÷(1/sin^2 theta)

= 1/cos^2 theta sin^2 theta÷(1/sin^2 theta)

= 1/cos^2 theta sin^2 theta * sin^2 theta/1

= 1/cos^2theta

= sec^2theta (Proved!)