" 7."quad sec alpha-1((2)/(sqrt(3)))

sec^(-1)((2sqrt(2))/(1+sqrt(3)))

If sec alpha=(2)/(sqrt3), the find the value of (1-"cosec "alpha)/(1+"cosec "alpha) , where alpha is in IV quadrant.

If tan alpha=(sqrt(3)+1)/(sqrt(3)-1) then the expression cos2 alpha+(2+sqrt(3))sin2 alpha is

For the principal values,evaluate the following: cot^(-1)(-1)+csc^(-1)(-sqrt(2))+secs^(-1)(2)cot^(-1)(-sqrt(3))+tan^(-1)(1)sec^(-1)((2)/(sqrt(3)))

If tan(alpha-beta)=1, sec(alpha+beta)=2/(sqrt(3) and alpha, beta are positive then the smallest value of alpha is

If tan (alpha - beta) = 1, "sec" (alpha + beta) = 2/(sqrt3) , find positive magnitude of alpha and beta .

If "cosec" (alpha - beta) = 2/(sqrt3) and "sec" (alpha + beta) = sqrt(2) , find least positive values of alpha and beta .

If tanalpha=(sqrt(3)+1)/(sqrt(3)-1) , then the expression cos 2alpha +(2+sqrt(3))sin 2alpha is