1. Use de Moivre's theorem to express sin50 in terms of powers of sine.

Q: Show that sin?(0) [1+ cot²(8)] = 1

A: Solve the given

Q: Using Euler' formula, show that sin 2x = 2 sin x cosx

A: Euler's Formula used.

Q: Find the exact value of tan [ 2 sin-1 (-12/13) ]

A: Given,  tan 2 sin-1-1213  We have to find the exact value of the above expression

Q: use demoirvre's Theorem of powers z= Square root 2 (cos 5 pi/24 +i sin 5 pi/24)

A: Given : z=2cos5π24+isin5π24 de moivre's theorem: If z=rcosθ+isinθ then zn=rncosnθ+isinnθ.

Q: prove sin2 a/2=csc a-cot a/2 csc a

A:

Q: Simplify arcsin(sin 6 7). 6 7I

A: We have to find the angle

Q: (a) State the sine rule and prove it in the case of an obtuse triangle.

A: Sine Rule/Law:-The Law of sine state that for any Triangle ABC , with sides a,b,c sinAa=sinBb=sinCc

Q: Give the exact value of sin(20).

A:

Q: Prove that sin? 0 + cosª 0 = sin“ 0 + cos² 0.

A: Using fundamental identity of trigonometry.