There is only 1 place to learn trigonometry

$\begin{aligned} \sin \theta &= \frac{1}{\csc \theta} \\ \cos \theta &= \frac{1}{\sec \theta} \\ \tan \theta &= \frac{1}{\cot \theta}. \end{aligned}$ $\begin{aligned} \sin \theta \csc \theta + \cos \theta \sec \theta + \tan \theta \cot \theta &= 1 + 1 + 1 \\ &= \boxed{3}. \end{aligned}$

If $\sin \theta \neq 0$ or $\cos \theta \neq 0$ the answer is 3.

Overrated problem factors are inverse each other. The best lesson is to watch and think before take the pencil.

1+1+1=3 as each term is the multiplication two trigonometric functions those are inverse to each other.

Sinx= 1/cscx,

Cosx=1/secx,

Tanx=1/cotx.

Therefore, sinxcosecx + cosxsecx + tanxcotx =1+1+1=3 which is the required ans.

1+1+1=3..... because sin, cos and tan are reciprocal terms of cosec, sec and cot respectively.

They are all inverse and cancel each other out to be 1. 1+1+1=3

Sin x csc = 1, cos x sec = 1, and tan x cot = 1. 1 + 1 + 1 = 3.

Becuse sin×csc =1 and cos×sec =1 and tan ×cot =1 so 1+1+1 =3 that is the ans

by definition cscΘ= 1/sinΘ secΘ= 1/cosΘ cotΘ= 1/tanΘ

So the problem simplifies to sinΘ(1/sinΘ)+cosΘ(1/cosΘ)+tanΘ(1/tanΘ) = 1+1+1 =3

an easy sum, cosecA= 1/sinA....secA=1/cosA......cotA=1/tanA.....SO WE GET 1+1+1 = 3

sin=1/csc, cos=1/sec, tan=1/cot (for an angle)
sin x csc=1, cos x sec=1, tan x cot=1
(sin x csc)+(cos x sec)+(tan x cot)=1+1+1=3