If `sqrt(2)cos A=cos B+cos^3B ,a n dsqrt(2)sinA=sinB-sin^3Bt h e nsin(A-B)=` `+-1` (b) `+-1/2` (c) `+-1/3` (d) `+-1/4`

If tanA.tanB=1/2,t h e n(5-3cos2A)(5-3cos2B)= (a)2 (b) 8 (c) 12 (d) 16

If cos^(-1)sqrt(p)+cos^(-1)sqrt(1-p)+cos^(-1)sqrt(1-q)=(3pi)/4, then the value of q is (a)1 (b) 1/(sqrt(2)) (c) 1/3 (d) 1/2

If tan A = (1-cos B)//sinB , then tan 2A = tan B.

If cos(alpha-beta)=3sin(alpha+beta),t h e n1/(1-3sin2alpha)+1/(1-3sin2beta)= (a) 1/2 (b) (-1)/2 (c) 1/4 (d) (-1)/4

If 2sec^2A-sec^4A-2cos e c^2A+cos e c^4A=(15)/4,t h e n tan A is equal 1//sqrt(2) (b) 1/2 (c) 1/2sqrt(2) (d) -1/(sqrt(2))

Prove that sin^2 A cos^2 B+cos^2 A sin^2 B+cos^2 A cos^2 B+sin^2 A sin^2 B=1

The least value of 2sin^2theta+3cos^2theta is 1 (b) 2 (c) 3 (d) 5

If x_1=3 and x_(n+1)=sqrt(2+x_n),ngeq1,t h e n""("lim")_(xrarroo)x_n is (a) -1 (b) 2 (c) sqrt(5) (d) 3

If cos(A-B)=3/5 and tan A tan B=2, then (a) cos A cos B=1/5 (b) sin A sin B=-2/5 (c) cos A cos B=-1/5 (d) sin A sin B=-1/5

("lim")_(xvecoo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 (b) 1 (c) 1/3 (d) 1/2