[" orilinates "x=(pi)/(4)" and "x=beta>(1)/(4)" is "(beta sin beta+(pi)/(4)cos beta+sqrt(2)beta)*" Ther "i((pi)/(2))" is - "],[[" (1) "((pi)/(4)+sqrt(2)-1)," (2) "(pi)/(4)-sqrt(2)+1," (3) "(1-(pi)/(4)-sqrt(2))," (4) "(1-(pi)/(4)+sqrt(2))]]

Let f(x) be a non-negative continuous function such that the area bounded by the curve y=f(x), the x -axis,and the ordinates x=(pi)/(4) and x=beta>(pi)/(4) is beta sin beta+(pi)/(4)cos beta+sqrt(2)beta Then f'((pi)/(2)) is ((pi)/(2)-sqrt(2)-1)( b) ((pi)/(4)+sqrt(2)-1)-(pi)/(2)( d) (1-(pi)/(4)-sqrt(2))

If 4 tan beta = 3 , then (4 sin beta - 3 cos beta)/( 4 sin beta + 3 cos beta)=

If 4tan beta=3, then (4sin beta-3cos beta)/(4sin beta+3cos beta)=

If tan alpha=(1)/(7) and sin beta=(1)/(sqrt(10)), where 0

If 2|sin2 alpha|=|tan beta+cot beta|,alpha,beta in((pi)/(2),pi) then the value of alpha+beta is (a) (3 pi)/(4) (b) pi(c)(3 pi)/(2) (d) (5 pi)/(4)

If sin alpha=(1)/(sqrt(10)) and sin beta=(1)/(sqrt(5)) then prove that alpha+beta=(pi)/(4)

If tan alpha=(x)/(x+1) andtan beta=(1)/(2x+1), then alpha+beta is equal to (pi)/(2) b.(pi)/(3) c.(pi)/(6) d.(pi)/(4), then alpha+beta

Prove that cos (alpha+beta) +sin (alpha-beta)=2sin(pi/4+alpha)cos(pi/4+beta)