If `tan alpha = 1/7, sin beta = 1/sqrt(10),` Prove that : `alpha + 2beta = pi/4`, where `0ltalpha lt pi/2 and 0ltbeta lt pi/2`.

If tan alpha=(1)/(7),sin beta=(1)/(sqrt(10)), prove that alpha+2 beta=(pi)/(4), where 0

lim alpha=(m)/(m+1),tan beta=(1)/(2m+1), prove that alpha+beta=(pi)/(4)

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

If alpha + beta and alpha - beta are solutions of theta for the equation tan^(2)theta - 4tan theta =-1 where 0 lt alpha lt pi/2 and 0 lt beta lt pi/2 then find alpha and beta .

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

If (1)/(cos alpha * cos beta )+ tan alpha * tan beta = tan gamma , where 0 lt gamma lt (pi)/2 and alpha , beta are positive acute angles , show that (pi)/4 lt gamma lt (pi)/2

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If cos (theta - alpha) = a and sin(theta - beta) = b (0 lt theta - alpha, theta - beta lt pi//2) , then prove that cos^(2) (alpha - beta) + 2ab sin (alpha - beta) = a^(2) + b^(2)