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Question

If tan  + sin  = m and tan  - sin  = n , Show that (m^2 – n^2 )^2 = 16 mn .

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Solution

(m²-n²)²

=>{(tanA + sinA)² - (tan A - sinA)²}²

=> {4tanAsinA}²

=>16tan²A sin²A

RHS:16(tanA+sinA)(tanA-sinA)

=>16 ( tan²A - sin²A)

=>16 (sin²A/cos²A - sin²A)

=>16 { (sin²A - sin²Acos²A)/cos²A}

=>16 sin²A(1 - cos²A)/cos²A

=>16 sin²Asin²A / cos²A

=>16tan²Asin²A

LHS=RHS


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