Assertion (A): {sin{\ }}^2\theta\le1 & {cos{\ }}^2\theta\le1 Reason (R): Hypotenuse is the longest

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Q.
$A s s e r t i o n (A) : {s i n}^{2} θ \leq 1 & {c o s}^{2} θ \leq 1$

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.
(1)

Hypotenuse is the longest side of the triangle.

$s i n θ = \frac{Opposite side}{Hypotenuse} < 1 and c o s θ = \frac{Adjacent side}{Hypotenuse} < 1 a n d h e n c e {s i n}^{2} θ \leq 1 & {c o s}^{2} θ \leq 1$

Thus, both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Solution

Q.
$A s s e r t i o n (A) : {s i n}^{2} θ \leq 1 & {c o s}^{2} θ \leq 1$

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.

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Solution

Q. Assertion (A): sin 2θ≤1 & cos 2θ≤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. (1) Hypotenuse is the longest side of the triangle. sinθ=Opposite sideHypotenuse<1andcosθ=Adjacent sideHypotenuse<1and hence sin 2θ≤1 &cos 2θ≤1 Thus, both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

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Q.
$A s s e r t i o n (A) : {s i n}^{2} θ \leq 1 & {c o s}^{2} θ \leq 1$

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