Question #09e1e

1 Answer
Jun 8, 2016

No 34 simplifies to 1

Explanation:

We make use of the following 'trig identities'

•cottheta=(costheta)/(sintheta)cotθ=cosθsinθ

• cos (angle) = sin (complement)

• sin (angle) = cos (complement)

Note Complementary angles are 2 angles whose sum is 90^@90

The complement of 60^@" is" (90-60)^@=30^@60 is(9060)=30

and so cos60^@=sin30^@cos60=sin30

rArrcos(90-theta)=sintheta" and" sin(90-theta)=costhetacos(90θ)=sinθ andsin(90θ)=cosθ

Substituting these identities into the question gives.

((costheta)/(sintheta).sintheta)/costheta=((costheta)/cancel(sintheta).cancel(sintheta))/costheta=costheta/costheta=1