Question

tan theta+cot theta= 1/sin theta cos theta

Answer 1

remember the identities that :
tanθ = sin θ /cos θ and
cot θ = cos θ /sin θ

Answer 2

what would be the identities equivalents for TAN and COT in terms of cosine and sine?

Answer 3

okay...

Answer 4

as RadEn just pasted, those are it, just ADD them up, get the LCD and add them up, see what you get

Answer 5

so the answer is what RadEn said?

Answer 6

well, no, replace tangent and cotangent, on the left-side, by what he said :)

Answer 7

$$
tan(\theta) = \cfrac{sin(\theta)}{cos(\theta)}\ \ \&\ \ \ cot(\theta) = \cfrac{cos(\theta)}{sin(\theta)}\ thus\\
\cfrac{sin(\theta)}{cos(\theta)}+\cfrac{cos(\theta)}{sin(\theta)} = \cfrac{}{\boxed{LCD?}}
$$

Answer 8

well, we have to prove the LHS can becomes like RHS
tanθ +cot θ
= sin θ /cos θ + cos θ /sin θ
= (sin^2 θ + cos^2 θ)/sinθcosθ
then use the identity :
sin^2 θ + cos^2 θ = 1
so,
= 1/sinθcosθ