I can't see photobucket images at the moment, so I shall leave
it to other helpful forumers like Mr Wee and ForbiddenSinner to
help you for that
If cosec x - sin x = a^3 and sec x - cos x = b^3, then
simplify the expression a^2b^2(a^2 + b^2) + 9. (Hint: the answer
should be a whole number)
we can change cosec x - sin x to sin²x/cos x and sec x - cos x
to cos² x /sin x
also, expand out a²b²(a² + b²)
to get a^4 from a³, just take (a³)^4/3, which is (sin²x/cos
x)^4/3
Do it for the other term
You will get a single trigo which you should be able to
simplify. But I didn't go and complete this out. Try it out and
show me where you are stucked.
Lastly, if sin x + sin y = p, cos x + cos y = q and theta is the
mean of x and y then find sin 2(theta).
Which means you are required to find sin (x+y). I can get
the answer, it is 2pq/ (p^2 + q^2) but only because this is a MCQ
question.
Tip:
pq = (sin x + sin y)(cos x + cos y) ===> somewhere along the
way, you will get sin² x + cos² x which gives you 1
Try it too :D
