`(a+2)sinalpha+(2a-1)cosalpha=(2a+1)iftanalpha"i s"` (a) `3/4` (b) `4/3` (c) `2a(a^2+1)` (d) `(2a)/(a^2-1)`

If cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x , then sinx is tan^2alpha/2 (b) cot^2alpha/2 (c) tan^2alpha (d) cotalpha/2

The value of cos(1/2cos^(-1)(1/8)) is (a) 3/4 (b) -3/4 (c) 1/(16) (d) 1/4

If pi,t h e nsqrt((1-cosalpha)/(1+cosalpha))+sqrt((1+cosalpha)/(1-cosalpha)) is equal to 2/(sinalpha) (b) -2/(sinalpha) (c) 1/(sinalpha) (d) -1/(sinalpha)

If sinalpha-sinbeta=1/3andcosbeta-cosalpha=1/2, show that cot(alpha+beta)/2=2/3

2tan^(-1)(-2) is equal to (a) -cos t^(-1)((-3)/5) (b) -pi+cos^(-1)3/5 (c) -pi/2+tan^(-1)(-3/4) (d) -picot^(-1)(-3/4)

The value of the integral int_0^1(dx)/(x^2+2xcosalpha+1) is equal to (a) sinalpha (b) alphasinalpha (c) alpha/(2sinalpha) (d) alpha/2sinalpha

If y^2=4b(x-c) and y^2 =8ax having common normal then (a,b,c) is (a) (1/2,2,0) (b) (1,1,3) (c) (1,1,1) (d) (1,3,2)

If (log)_4 5=aa n d(log)_5 6=b , then (log)_3 2 is equal to 1/(2a+1) (b) 1/(2b+1) (c) 2a b+1 (d) 1/(2a b-1)

The greatest value of sin^4theta+cos^4thetai s 1/2 (b) 1 (c) 2 (d) 3

The value of ("lim")_(xvecpi)(1+cos^3x)/(sin^2x)i s 1/3 (b) 2/3 (c) -1/4 (d) 3/2