Question

Assertion :Consider the following statements.
The value of $\sin {120}^o$ can be derived by taking $\theta ={240}^o$ in the equation $2\sin \frac{\theta }{2}=\sqrt{1+\sin \theta }-\sqrt{1-\sin \theta }$. Reason: The angles A, B, C and D of any quadrilateral ABCD satisfy the equation $\cos \left(\frac{1}{2}\right(A+C\left)\right)+\cos \left(\frac{1}{2}\right(B+D\left)\right)=0$
Then the truth value of p and q are respectively.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

By half angle formulas $\sin \theta /2$ and be calculated by $\sin \theta$

The angles of quadrilateral satisfies the equation $\cos \left(\frac{1}{2}\right(A+C\left)\right)+\cos \left(\frac{1}{2}\right(B+D\left)\right)=0$

But they have no relation among them .