Question

If \( \sin \theta + \csc \theta = 2 \), then the value of \( \sin^{10} \theta + \csc^{10} \theta \) is

• A. 2
• B. \( 2^4 \)
• C. \( 2^8 \)
• D. \( 2^{10} \)

Hint:

For such trigonometric equations, recognize key identities and solve step by step to find the simplified value.

Answer 1

The Correct Option is A

From the given equation \( \sin \theta + \csc \theta = 2 \), we have \( \sin \theta = 1 \) and \( \csc \theta = 1 \). Hence, the value of \( \sin^{10} \theta + \csc^{10} \theta = 2 \).