`sin (pi/2) = 2 sin(pi/4) cos (pi/4)`

sin pi/3 = 2sin pi/6 cos pi/6

Prove that (i) "sin " (7pi)/(12) " cos " (pi)/(2) - "cos " *(7pi)/(12) " sin " (pi)/(4) = (sqrt(3))/(2) (ii) " sin " (pi)/(4) " cos " (pi)/(2) + "cos"(pi)/(4) " sin " (pi)/(12) = (sqrt(3))/(2) (iii) " cos " (2pi)/(3) " cos " (pi)/(4) - " sin " (2pi)/(3) " sin " (pi)/(4) =(-(sqrt(3) +1))/(2sqrt(2))

Using application of trignometric formulas prove that (i)cos(pi/4+x)+cos(pi/4-x)=sqrt2cos x(i1)sin(7pi/12)cos(pi/4)-cos(7pi/12)sin(pi/4)

sin(pi/4+A).sin(pi/4-A)=1/2 cos2A

Prove that (i) " tan"^(2) .(pi)/(3) + 2cos^(2) .(pi)/(4)+ 3 sec^(2).(pi)/(6)+ 4 cos^(2).(pi)/(2)=8 (ii) " sin ".(pi)/(6) " cos 0 + sin ".(pi)/(4) " cos " .(pi)(4) + " sin " .(pi)/(3) "cos " .(pi)/(6) =(7)/(4) (iii) " 4sin " (pi)/(6) " sin"^(2) (pi)/(3) + 3 " cos " .(pi)/(3) " tan ".(pi)/(4) = " cosec"^(2).(pi)/(2)=4

Prove that (i) cos (n + 2) x cos (n+1) x +sin (n+2) x sin (n+1) x = cos x) (ii) " cos " .((pi)/(4)-x) " cos " .((pi)/(4)-y) " - sin " ((pi)/(4)-x ) " sin " ((pi)/(4) -y) =" sin " (x+y)

Numerical value of cos ((pi) / (12)) ((sin (5 pi)) / (12) + cos ((pi) / (4))) + sin ((pi) / (12)) (( cos (5 pi)) / (12) -sin ((pi) / (4)))

The least positive integer n such that [{:(cos""(pi)/(4), sin""(pi)/(4)) ,(- sin ""(pi)/(4) , cos ""(pi)/(4)):}]^(n) is an identity matrix of order 2 is

Prove that (a) sin^(2)(pi/6) + cos^(2)( pi/3) - tan^(2)(pi/4) = -1/2 (b) sin((8pi)/3) cos((23pi)/6) + cos((13pi)/3) sin((35pi)/6) = 1/2