Assertion (A): If {sin{\ }}^2\theta\le\frac{1}{2}, then \frac{1}{\sqrt2}\le cos{\theta}<1 Reason (R): Hypotenuse is the longest side of the triangle

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Q.
Assertion (A): If ${s i n}^{2} θ \leq \frac{1}{2}, t h e n \frac{1}{\sqrt{2}} \leq c o s θ < 1$ .

Reason (R): Hypotenuse is the longest side of the triangle.

1 Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

2 Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

3 Assertion (A) is true but reason (R) is false.

4 Assertion (A) is false but reason (R) is true.

Ans.
(4)

Assertion (A) is false because if ${s i n}^{2} θ \leq \frac{1}{2},$ then $\sin θ$ can be equal to 0. In that case, cosθ will be equal to 1 $(w h e n θ = 0 °) .$ . However, in the Assertion, the equality sign on cosθ is missing. Hence the Assertion is false.

Solution

Q.
Assertion (A): If ${s i n}^{2} θ \leq \frac{1}{2}, t h e n \frac{1}{\sqrt{2}} \leq c o s θ < 1$ .

Reason (R): Hypotenuse is the longest side of the triangle.

1 Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

2 Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

3 Assertion (A) is true but reason (R) is false.

4 Assertion (A) is false but reason (R) is true.

Ans.
(4)

Assertion (A) is false because if ${s i n}^{2} θ \leq \frac{1}{2},$ then $\sin θ$ can be equal to 0. In that case, cosθ will be equal to 1 $(w h e n θ = 0 °) .$ . However, in the Assertion, the equality sign on cosθ is missing. Hence the Assertion is false.

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Solution

Q. Assertion (A): If sin 2θ≤12, then 12≤cosθ<1. Reason (R): Hypotenuse is the longest side of the triangle.

1 Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

2 Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

3 Assertion (A) is true but reason (R) is false.

4 Assertion (A) is false but reason (R) is true.

Ans. (4) Assertion (A) is false because if sin 2θ≤12, then sin θ can be equal to 0. In that case, cosθ will be equal to 1(when θ=0°).. However, in the Assertion, the equality sign on cosθ is missing. Hence the Assertion is false.

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Q.
Assertion (A): If ${s i n}^{2} θ \leq \frac{1}{2}, t h e n \frac{1}{\sqrt{2}} \leq c o s θ < 1$ .

Reason (R): Hypotenuse is the longest side of the triangle.

Ans.
(4)

Assertion (A) is false because if ${s i n}^{2} θ \leq \frac{1}{2},$ then $\sin θ$ can be equal to 0. In that case, cosθ will be equal to 1 $(w h e n θ = 0 °) .$ . However, in the Assertion, the equality sign on cosθ is missing. Hence the Assertion is false.