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trigo math

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7. Prove that tan B sin B + cos B = sec B.

11. Prove that tanλ cos^2λ +sin^2λ/sinλ = cos λ + sin λ.

12. Prove that 1+tanθ/1+tanθ = sec^2θ+2tanθ/ 1-tan^2θ.

21. Prove that sin^2w-cos^2w/ tan w sin w + cos w tan w = cos w – cot w cos w.

  • trigo math -

    tan*sin+cos
    = sin^2/cos + cos
    = (sin^2+cos^2)/cos
    = 1/cos
    = sec

    (tan*cos^2 + sin^2)/sin
    = (sin*cos + sin^2)/sin
    = sin(cos+sin)/sin
    = cos+sin

    I think you mean
    (1+tan)/(1-tan)
    = (1+tan)^2/(1-tan^2)
    = (1+2tan+tan^2)/(1-tan^2)
    = (sec^2+2tan)/(1-tan^2)

    the last one needs some parentheses. Too complicated and ambiguous

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