Evaluate|[cosalpha cosbeta,cosalpha sinb...

Evaluate`|[cosalpha cosbeta,cosalpha sinbeta,-sinalpha],[-sinbeta,cosbeta,0],[sinalpha cosbeta,sinalpha sinbeta,cosalpha]|`

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If cosalpha+cosbeta=0=sinalpha+sinbeta,cos2alpha+cos2beta is equal to a) -2sin(alpha+beta) b) 2cos(alpha+beta) c) 2sin(alpha-beta) d) -2cos(alpha+beta)

Using properties of determinants, prove that |[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,cosbeta,cos(beta+delta)],[singamma,cosgamma,cos(gamma+delta)]| = 0

If Delta=|(sinalpha,cosalpha,sin(alpha+delta)),(sinbeta,cosbeta,sin(beta+delta)),(singamma,cosgamma,sin(gamma+delta))| then Delta is independent of a) delta only b) alpha, beta, gamma only c) alpha,beta,gamma,delta d)None of these

If f(alpha,beta)=|(cosalpha,-sinalpha,1),(sin alpha,cosalpha,1),(cos(alpha+beta),-sin(alpha+beta),1)| , then a) f(300,200) ne f(400, 200) b)f(200,400) = f(200,600) c)f(100,200) =f(200,200) d)None of these

If A_(alpha)=[(cos alpha,sinalpha),(-sinalpha,cosalpha)] then A_(alpha) A_(beta) is equal to A) A_(alpha beta) B) A_(alpha +beta) C) A_(alpha - beta) D)None of these

int(1)/(sqrt(sin^(3)xsin(x+alpha)))dx,alpha!=npi,nin Z is equal to a) -2" cosec "alpha(cosalpha-tanxsinalpha)^(1//2)+C b) -2(cosalpha+cotxsinalpha)^(1//2)+C c) -2" cosec "alpha(cosalpha+cotxsin alpha)^(1//2)+C d) -2" cosec "alpha(sinalpha+cotxcosalpha)^(1//2)+C

If sinalpha=15/17 , cosbeta=12/13 and alpha and beta are in the first quadrant , find the values of sin(alpha+beta) , cos(alpha+beta) , and tan(alpha+beta)

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