PLEASE HELP QUICK. Show that sin(90-θ) = cosθ (where a right angle triangle has sides b and a and hypotenuse c, where b is longer than a)

Question

PLEASE HELP QUICK. Show that sin(90-θ) = cosθ (where a right angle triangle has sides b and a and hypotenuse c, where b is longer than a) <- nothing complicated, just described the picture

anonymous · Answer

I don't get this (θ-90) or (180-θ) kind of stuff D:

hartnn · Answer

u know the formula for sin (A+B) = ?

anonymous · Answer

i forgot but i found that: sin(A+B)=sin A cos B + cos A sin B

hartnn · Answer

thats correct..

anonymous · Answer

oh and more useful for this - sin(A-B)=sin A cos B - cos A sin B

hartnn · Answer

and sin (A-B) = ?

hartnn · Answer

good

hartnn · Answer

now put A = 90 and B = theta in that

hartnn · Answer

ok, are u required to do this using triangle ??

anonymous · Answer

here the question

hartnn · Answer

oh, yes.. u need to use that triangle.

hartnn · Answer

name all the vertices  of triangle as A,B,C
can u ?

anonymous · Answer

yea sure

anonymous · Answer

vertice B is opposite to the side b so between sides a and c. same for the others

hartnn · Answer

yup, now angle A =theta, angle C = 90
can u find angle B in terms of theta ?

anonymous · Answer

angle B is the same as 180-90-theta

hartnn · Answer

which is ?

anonymous · Answer

90-theta

hartnn · Answer

now can u find cos theta from that triangle ?
in terms of a,b,c ?

anonymous · Answer

sin(90-theta) is sin(B) is b/c

anonymous · Answer

cos(theta) b/c

anonymous · Answer

LHS = RHS ! :)

hartnn · Answer

great, u can prove other two the same way

anonymous · Answer

i understand the answer, but is there some technicality in how i proceeded with getting the answer that could make me lose marks?

anonymous · Answer

in either case thank you in advance for helping me get this, it was a great help

hartnn · Answer

nothing incorrect in what we did., u cannot loose marks with this method.

anonymous · Answer

okay, thank you!