Question

cos theta÷sin(90°+ theta)+sin(- theta)÷ sin(180+ theta)- tan(90+ theta)÷cot theta =3​

Answer 1

do it yourself I think own

Answer 2

Acc. to me,

Here i supposed your theta =x

Your question,

cos x/sin(90+x) + sin(-x)/sin(180+x) -tan(90+x)/cotx

First of all you know about sign in quadrant

In first Quadrent all trignometry function is positive

In second only sin,cosec is positive

in third only tan, cot is positive

In forth only cos,sec is positive

And also Know how to go which quadrant

So here

1.sin(90+x)=means more than 90° so 2nd quadrant,in 2nd sin is + and by 90 it change into cos

so sin(90+x)=cosx

2.sin(-x)= -sinx (see rule in book)

3.sin(180+x)= -sinx [here 180+ means x go more than 180 and go in 3rd quad. there sin is not positive(see above) means negative.here 180 so no change to cos (on change when 90 or 270)].

4.tan(90+x)= -cotx [here 90 means chango to cot , 90+ means more than 90 (second quad.) where tan is -ve]

put all values in question,

cosx/cosx + (- sinx)/(-sinx) - (-cotx)/cotx

when you solve you found

1 + 1 + 1 =3

so L.H.S =R.H.S

I hope you understand