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(90−60)∘=30∘ and so
cos60^@=sin30^@cos60∘=sin30∘
rArrcos(90-theta)=sintheta" and" sin(90-theta)=costheta⇒cos(90−θ)=sinθ andsin(90−θ)=cosθ Substituting these identities into the question gives.
((costheta)/(sintheta).sintheta)/costheta=((costheta)/cancel(sintheta).cancel(sintheta))/costheta=costheta/costheta=1
