Question 20 - CBSE Class 10 Sample Paper for 2026 Boards - Maths Standard [Term I] - Solutions of Sample Papers for Class 10 Boards

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Question 20 Assertion (A): If cos𝐴+cos^2 𝐴=1, then sin^2 𝐴+sin^4 𝐴=1 Reason (R): sin^2 𝐴+cos^2 𝐴=1 Choose the correct option: (A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (B) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) (C) Assertion (A) is true but reason (R) is false. (D) Assertion (A) is false but reason (R) is true.Checking Assertion If cos𝐴+cos^2 𝐴=1, then sin^2 𝐴+sin^4 𝐴=1 Given, cos 𝐴+cos^2 𝐴=1 𝑐𝑜𝑠 𝐴=1−〖𝑐𝑜𝑠〗^2 𝐴 𝒄𝒐𝒔 𝑨=〖𝐬𝐢𝐧〗^𝟐⁡𝑨 Now, sin^2 𝐴+sin^4 𝐴 = sin^2 𝐴+(〖𝒔𝒊𝒏〗^𝟐 𝑨)^𝟐 Putting sin2 A = cos A = cos⁡𝐴+(cos⁡𝐴 )^2 = 𝒄𝒐𝒔⁡𝑨+〖𝐜𝐨𝐬〗^𝟐⁡𝑨 Given 𝑐𝑜𝑠𝐴+〖𝑐𝑜𝑠〗^2 𝐴=1 = 1 Thus, the Assertion is true Checking Reason sin^2 𝐴+cos^2 𝐴=1 This identitiy is always true Thus, Reason is true. Is Reason correct explanation for Assertion? Since we used sin^2 𝐴+cos^2 𝐴=1 to prove Assertion is true Therefore, Reasoning is correct explanation for Assertion So, Assertion is true Reasoning is true and, Reasoning is a correct explanation for Assertion So, the correct answer is (a)