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Introduction to Trigonometry
CH08 Question Bank
CBSE_CH08_QUESTION_BANK
Grade 10
Question:
Assertion (A): For an acute angle $A$, $\sec^2A-\tan^2A=1$. Reason (R): This follows directly by dividing the identity $\sin^2A+\cos^2A=1$ throughout by $\cos^2A$.
Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A. Both Assertion (A) and Reason (R) are true, but R is NOT the correct explanation of A. Assertion (A) is true, but Reason (R) is false. Assertion (A) is false, but Reason (R) is true.
Step-by-Step Solution
Key Concept: Standard derivation of a secondary trigonometric identity from the primary one.
$\sec^2A-\tan^2A=(1+\tan^2A)-\tan^2A=1$, confirming A is true. [0.5 Mark]
R correctly describes exactly how this identity is derived (dividing $\sin^2A+\cos^2A=1$ by $\cos^2A$ gives $\tan^2A+1=\sec^2A$, which rearranges to A), so R correctly explains A. [0.5 Mark]
Correct Answer:Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
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