Question

Assertion A : In a right angled triangle ${\sin }^{2}A+{\sin }^{2}B+{\sec }^{2}C=2$
Reason R: lf $\alpha ,\beta$ are complementary angles , then ${\sin }^2\alpha +{\sin }^2\beta =1$

• A. A and R are true and R is the correct explanation of A.
• B. A and R are true and R is not the correct explanation of A.
• C. A is true, R is false.
• D. A is false, R is true.

Answer 1

The correct option is D A is false, R is true.

In a right angled triangle ${\sin }^{2}A+{\sin }^{2}B+{\sin }^{2}C=2$
but given that,${\sin }^{2}A+{\sin }^{2}B+{\sec }^{2}C=2$
$\Rightarrow {\sin }^{2}C={\sec }^{2}C$ which is not possible.
Assertion is false.
lf $\alpha ,\beta$ are complementary angles then ${\sin }^2\alpha +{\sin }^2\beta =1$
$\therefore$ Assertion is false, Reason is true.
Hence, option D.