If `sin alpha = 3/5`, where `(pi)/2 lt alpha lt pi`, evaluate `cos 3 alpha`.

If 20 sin^(2) alpha+21 cos alpha-24=0 where (7pi)/(4) lt alpha lt 2pi then cot alpha//2=

If cos alpha = (-3)/5 and sin beta = 7/25 where (pi)/2 lt alpha lt pi and 0 lt beta lt (pi)/2 then find the values of tan (alpha + beta) and sin (alpha + beta) .

If sec alpha = (13)/(5) " where " alpha lt 90^(@) , then the value of (2-3 cot alpha )/(4-9 tan alpha ) =

If 0 lt alpha lt (pi)/(6) then alpha(cosec alpha) is

Statement I: If sin alpha = 12/13, (0 lt alpha lt pi/2) and cos beta =-3/5,(pi lt beta lt (3pi)/2) , then sin(alpha + beta) = 56/65 Statement II : If theta and phi , are angles in the first quadrant such that tan theta =1/7 and sin phi =1/sqrt(10) , then theta + 2phi = 45^(@) Which of the above statements is correct?

Let cos beta is the geometric mean between sin alpha and cos alpha , where 0 lt alpha lt beta lt pi//2 , then cos 2beta is equal to

( sin alpha sin 3alpha + sin 3alpha sin 7 alpha + sin 5 alpha sin 15 alpha )/( sin alpha cos 3 alpha + sin 3alpha cos 7 alpha + sin 5 alpha cos 15 alpha ) =