`cos ((3pi )/( 2 ) + x) cos (2pi + x) [cot ((3pi)/( 2)- x ) + cot (2pi +x) ]=1`

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

The value of cos y cos ((pi)/(2) - x) - cos ((pi)/(2) - y) cos x + sin y cos ((pi)/(2) - x) + cos x sin ((pi)/(2) - y) is zero if

cos ((3pi)/( 4) + x) - cos((3pi)/( 4) -x) =- sqrt2 sin x

The number of solutions of the equation cos^(2) (x + (pi)/( 6)) + cos ^(2) x - 2 cos ( + (pi)/( 6)) co ""(pi)/( 6) = sin ^(2) (pi)/( 6) in interval ((-pi)/( 2), (pi)/( 2)) is _____

The period of sin ((pi x )/( 2 )) + 2 cos ((pi x)/( 3 ) ) - tan ((pi x)/(4)) is

sin""((pi)/2+ theta ) * cos (pi- theta ) * cot ""((3pi)/(2)+ theta ) - sin""((pi)/2- theta ) * sin""((3pi)/2 - theta ) * cot ""((pi)/2 + theta ) =

Find the extreme values of the following function over R. (i) sin^(2) (60^(0) + x) + sin^(2) (60^(0) - x) (ii) cos (x+ (Pi)/(3) ) + 2sqrt(2) sin (x+ (pi)/(3))-3 (iii) 3 sin^(2) x+ 5 cos^(2) x (iv) cos 2 x+ cos^(2) x (v ) cos x cos ((2pi)/(3) + x) cos ((2pi)/(3)-x)

The sum of the solutions in (0, 2pi) of the equation cos x cos ((pi)/(3)-x)cos((pi)/(3)+x)=(1)/(4) is

Solve tan 2x =- cot (x + (pi)/(3))

Lt_(x to 1) (1+sin pi x)^(cot pi x)=