If tan A = 2/3 find the value of (3sin A + 4 cos A)/ (3sin A – 4 cosA) (A) - 3 (B) - 4 (C) - 5 (D) none of these 8. sin2 1 + sin2 3 + sin2 5 + sin2 7 + ……… + sin2 89 =

(A) -3 (3sin A + 4 cos A)/ (3sin A – 4 cosA) Divide Numerator and Denominator by cos A to get: (3tan A + 4 )/ (3tan A – 4) Substitute the value of tan A to get the final answer as -3..

Sin2 1 + sin2 3 + ... + sin2 45 + ... + sin2 87 + sin2 89 = sin2 1 + sin2 3 + ... + 1/2 + ... + sin2 (90-3) + sin2 (90-1) = sin2 1 + sin2 3 + ... + 1/2 + ... + cos2 87 + cos2 89 Grouping the sin2x + cos2x terms, = (sin2 1 + cos2 1) + (sin2 3 + cos2 3) + ... + 1/2 There will be 23 such terms, which are all = 1 = 1+1+1+...23 times + 1/2 =23+1/2 =47/2

rationalise them and take 16 cos(square)A common from numerator and denominator and cancel out. now put the value of tanA