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

Question

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

in progress 0
Yến Oanh 3 months 2021-07-28T15:20:00+00:00 1 Answers 1 views 0

Answers ( )

    0
    2021-07-28T15:21:23+00:00

    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!)

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )