" I."sin^(-1)(-(1)/(2))quad " 2.cos "

Prove that (i) " 2 cos " 45^(@) " cos " 15^(@)=((sqrt(3)+1))/(2) " "(ii) 2 " sin " 75^(@) " sin " 15^(@)=(1)/(2) (iii) " cos " 15^(@) - " sin " 15 =(1)/(sqrt(2))

(i) Evaluate : sec (cos^(-1).(1)/(2)) (ii) slove the equations sin^(-1) x + sin^(-1) y = (2pi)/(3) and cos^(-1) x - cos ^(-1) y = (pi)/(3)

For the principal values, evaluate each of the following : (i) sin^(-1)(-1/2)+2cos^(-1)(-(sqrt(3))/2) (ii) sin^(-1)(-(sqrt(3))/2)+cos^(-1)((sqrt(3))/2)

(i) (1)/(sin^(2)a)-(1)/(sin^(2)B)=(cos^(2) a-cos^(2) B)/(sin^(2)a*sin^(2) B)

Simplify (i) sin(pitan{cot^(-1)((-2)/3)}) (ii) sin(2"tan"^(-1)1/2) (iii) cos(2cos^(-1)(1//5)+sin^(-1)(1//5))

Simplify (i) sin(pitan{cot^(-1)((-2)/3)}) (ii) sin(2"tan"^(-1)1/2) (iii) cos(2cos^(-1)(1//5)+sin^(-1)(1//5))

For the principal values, evaluate each of the following : (i) cos^(-1) (1/2)+2sin^(-1) (1/2) (ii) cos^(-1)(1/2)-2sin^(-1)(-1/2)

{ cos (sin ^(-1) x)}^(2) ={sin (cos ^(-1) x)}^(2)

Evaluate: (i) inttan^(-1)((sin2x)/(1+cos2x))\ dx (ii) intcos^(-1)(sinx)\ dx

Evaluate: (i) intcot^(-1)((sin2x)/(1-cos2x))\ dx (ii) intsin^(-1)((2tanx)/(1+tan^2x))\ dx