Assertion :If 0<α<(π/4), then the equation (x−sinα)(x−cosα)−2=0 has both roots in (sinα,cosα). Reason: If f(a) and f(b) possess opposite signs, then there exists at least one solution of the equation f(x)=0 in open interval (a,b).
A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution
The correct option is D Assertion is incorrect but Reason is correct Reason is true. Assertion:f(x)=(x−sinα)(x−cosα)−2f(sinα)=−2<0f(cosα)=−2<0. Then there exists no roots in (sinα,cosα).