Trigonometry

To find the value of $A%20%3D%20%5Csin%5Ctheta%20%5Ccos%5Ctheta%20%5Ctan%5Ctheta%20%2B%20%5Csin%5Ctheta%20%5Ccos%5Ctheta%20%5Ccot%5Ctheta$ , we start by simplifying each term of the expression.
The trigonometric identities: $%5Ctan%5Ctheta%20%3D%20%5Cfrac%7B%5Csin%5Ctheta%7D%7B%5Ccos%5Ctheta%7D$ and $%5Ccot%5Ctheta%20%3D%20%5Cfrac%7B%5Ccos%5Ctheta%7D%7B%5Csin%5Ctheta%7D$ can be used. Plug these into the expression:
$A%20%3D%20%5Csin%5Ctheta%20%5Ccos%5Ctheta%20%5Cleft(%5Cfrac%7B%5Csin%5Ctheta%7D%7B%5Ccos%5Ctheta%7D%5Cright)%20%2B%20%5Csin%5Ctheta%20%5Ccos%5Ctheta%20%5Cleft(%5Cfrac%7B%5Ccos%5Ctheta%7D%7B%5Csin%5Ctheta%7D%5Cright)$
Simplify each term:
- $%5Csin%5Ctheta%20%5Ccos%5Ctheta%20%5Ccdot%20%5Cfrac%7B%5Csin%5Ctheta%7D%7B%5Ccos%5Ctheta%7D%20%3D%20%5Csin%5E2%5Ctheta$
- $%5Csin%5Ctheta%20%5Ccos%5Ctheta%20%5Ccdot%20%5Cfrac%7B%5Ccos%5Ctheta%7D%7B%5Csin%5Ctheta%7D%20%3D%20%5Ccos%5E2%5Ctheta$
So, $A%20%3D%20%5Csin%5E2%5Ctheta%20%2B%20%5Ccos%5E2%5Ctheta$ .
According to the Pythagorean identity, $%5Csin%5E2%5Ctheta%20%2B%20%5Ccos%5E2%5Ctheta%20%3D%201$ . Therefore, the value of $A$ is 1.

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Trigonometry

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs