Question

Given that A=\( (sin\theta cos\theta tan\theta + sin\theta cos\theta cot\theta)\), the value of A is

Answer 1

Correct Answer: 1

To find the value of \( A = \sin\theta \cos\theta \tan\theta + \sin\theta \cos\theta \cot\theta \), we start by simplifying each term of the expression. 
The trigonometric identities: \(\tan\theta = \frac{\sin\theta}{\cos\theta}\) and \(\cot\theta = \frac{\cos\theta}{\sin\theta}\) can be used. Plug these into the expression: 
\(A = \sin\theta \cos\theta \left(\frac{\sin\theta}{\cos\theta}\right) + \sin\theta \cos\theta \left(\frac{\cos\theta}{\sin\theta}\right)\) 
Simplify each term: 
- \(\sin\theta \cos\theta \cdot \frac{\sin\theta}{\cos\theta} = \sin^2\theta\) 
- \(\sin\theta \cos\theta \cdot \frac{\cos\theta}{\sin\theta} = \cos^2\theta\)
So, \(A = \sin^2\theta + \cos^2\theta\).
According to the Pythagorean identity, \(\sin^2\theta + \cos^2\theta = 1\). Therefore, the value of \(A\) is 1.