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Answer 1 · 2017-11-20T02:51:12

#cos^2(C)-cos^2(D) = sin^2(D) - sin^2(C)#

A common formula used all the time in trigonometry is

#sin^2(theta)+cos^2(theta)=1#

Subtracting the #sin^2(theta)# from both sides gives

#cos^2(theta)=1-sin^2(theta)#

This means that the formula #cos^2(C)-cos^2(D)# can be expressed as

#cos^2(C)-cos^2(D) = (1-sin^2(C))-(1-sin^2(D))#

#=-sin^2(C)+sin^2(D)#

#=sin^2(D) - sin^2(C)#

Answer 2 · 2017-11-20T02:51:16

#-sin^2C+sin^2D#

If you meant to ask how to turn the expression into something in terms of a sine functions this is how:

We know:

#sin^2x+cos^2x=1#

If we subtract #sin^2x# from both sides we get:

#sin^2x+cos^x-sin^2x=1-sin^2x#

#cos^2x=1-sin^2x#

Therefore:

#1-sin^2C-(1-sin^2D)=1-sin^2C-1+sin^2D=cancel1-sin^2Ccancel-1+sin^2D=-sin^2C+sin^2D#