Question

sin (90-A)and cos A are​

Answer 1

Step-by-step explanation:

Take a look at the diagram below:

enter image source here

It's a generic right triangle, with a

90

o

angle as indicated by the little box and an acute angle

a

. We know the angles in a right triangle, and a triangle in general, must add to

180

o

, so if we have an angle of 90

and an angle of a

, our other angle must be

90−a :(a)+(90−a)+(90)180=180

We can see that the angles in our triangle do indeed add to

180

, so we're on the right track.

Now, let's add some variables for side length onto our triangle.

enter image source here

The variable

s

stands for the hypotenuse,

l stands for length, and h stands for height.

We can start on the juicy part now: the proof.

Note that

sin a , which is defined as opposite ( h) divided by hypotenuse ( s ) , equals hs in the diagram:sin a=hs

Note also that the cosine of the top angle,

90−a , equals the adjacent side ( h ) divided by the hypotenuse ( s ):cos(90−a)=hs

So if sin a=hs , and cos(90−a)=hs ...Then sin a must equal cos(90−a) !sina=cos(90−a)

And boom, proof complete.

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