Q. 513.8( 6 Votes )

If 7 sin A + 24 cos A = 25, find the value of tan A.

Answer :

Given : 7 sin A + 24 cos A = 25

Squaring both the sides, we get


(7 sin A + 24 cos A)2 = 625


49 sin2 A +576 cos2 A + 2(7sin A) (24cos A) = 625 [ (a + b)2 =a2 +b2 +2ab]


49 sin2 A +576 cos2 A + 336 cosA sinA = 625


Divide by cos2 θ, we get



49tan2 A +576+ 336 tanA = 625sec2 A


49tan2 A +576+ 336 tanA = 625(1 + tan2 A) [ 1+ tan2θ = sec2 θ]


49tan2 A +576+ 336 tanθA = 625+625 tan2 A


576tan2 A – 336tanA + 49 = 0


576tan2 A – 168 tanA – 168 tanA +49 = 0


24tanθ (24tan A 7) 7(24tan A 7) = 0


(24tan A – 7)2 = 0



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