if cosA-sinA=√2 sinA then proove that cosA+sinA=√2cosA​

Question

if cosA-sinA=√2 sinA
then proove that cosA+sinA=√2cosA​

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Josephine 5 months 2021-12-13T02:30:14+00:00 1 Answer 0 views 0

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    2021-12-13T02:31:35+00:00

    Answer:

    Step-by-step explanation:

    (cosA-sinA)=√2 sinA      

    (cosA- sinA)/sinA = √2

    cotA – 1 = √2

    cotA = (√2 +1)  ……..(i)

    cosA+sinA=√2cosA​

    (cosA+sinA)/cosA = √2

    1 + tanA = √2

    tanA = √2 – 1

    1/cotA = √2 – 1

    1/(√2 +1)  = (√2 – 1)

    1 = (√2 – 1)(√2 +1)

    1=1

    hence proved LHS = RHS

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