If tan x=n tan y and sin x = msin y, prove that cos-x= m-1 m-1 ​

Question

If tan x=n tan y and sin x = msin y, prove that cos-x=
m-1
m-1

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Natalia 1 month 2021-10-10T12:46:26+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-10T12:47:34+00:00

    Step-by-step explanation:

    tan x / tan y = n  ⇒ n^2 = tan^2 x / tan^2 y

                                  n^2 – 1 = tan^2 x – tan^2 y / tan^2y

    similarly                  m^2 – 1 = sin^2 x – sin^2 y / sin^2y

    m^2 – 1 /  n^2 – 1 =   ( sin^2 x – sin^2 y )( tan^2y)  /   ( tan^2 x – tan^2 y )sin^2y

                   =  ( sin^2 x – sin^2 y ) (  1 / cos^2 y )  / sec^2x – sec^2 y

          =   ( sin^2 x – sin^2 y ) (  1 / cos^2 y ) / cos ^2y – cos^2x / cos^2xcos^2y

            = cos^2 x    

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