Trigonometry Formula Show/Hide

1. Express \( \sin2\theta \) in terms of \(\sin\theta\) and \(\cos\theta \).

Solution:
\(\sin2\theta = 2\sin\theta \cos\theta\)

2. Express \( \sin2\theta \) in terms of \(\tan\theta\).

Solution:
\(\sin2\theta = \frac{2\tan\theta}{1-\tan^2\theta}\)

4. Simplify: Express \(\cos2\theta \) in terms of \(\cos\theta \).

Solution:
\(\cos2\theta=2\cos^2\theta - 1\)

5. Define sub multiple angle with an example.

Solution:
If \( A \) be any angle, then \( \frac{A}{2}, \frac{A}{3}... \) etc. are called sub-multiple angles of A.

6. Prove that: \( \frac{\sin \theta }{1+ \cos \theta} = \tan \frac{\theta}{2} \)

Solution:
\begin{align} \text{ LHS } \ & = \frac{\sin \theta }{1+\cos \theta}\\ \ \ & = \frac{2\sin \frac{\theta}{2} \cos \frac{\theta}{2} }{1+ 2\cos^2 \frac{\theta}{2} -1 }\\ \ \ & = \frac{2 \sin \frac{\theta}{2} \cos \frac{\theta}{2} }{2\cos^2 \frac{\theta}{2} } \\ \ \ & = \frac{ \sin \frac{\theta}{2} }{ \cos \frac{\theta}{2} } \\ \ \ & = \tan \frac{\theta}{2} \\ \ \ & = \text { RHS } \end{align}

7. Write \(\sin A \) in terms of \(\frac{A}{2}\)

Solution: