Question 10 a and b how to do plz?

year 11 haese specialist mathematicsyear 11 haese specialist mathematics

1 Answer
Nov 7, 2017

PROOF:

Explanation:

Double angle identities:
sin2x=2sinxcosxsin2x=2sinxcosx
cos2x= cos^2 x – sin^2 x

We also know that:
sintheta=("opposite")/("hypotenuse")
costheta=("adjacent")/("hypotenuse")

Based on the given triangle,
sintheta=b/c
costheta=a/c

sin2theta=2sinthetacostheta
sin2theta=2*b/c*a/c
sin2theta=(2ab)/c^2

cos2theta= cos^2theta – sin^2theta
cos2theta= (a/c)^2 – (b/c)^2
cos2theta= a^2/c^2 – b^2/c^2
cos2theta= [a^2 – b^2]/c^2