Assertion (A): {csc{\ }}^2{45}^\circ-{cot{\ }}^2{45}^\circ=1 Reason (R): {csc{\ }}^2\theta-{cot{\ }}^2

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Solution

Q.
$A s s e r t i o n (A) : {c s c}^{2} 45 ° - {c o t}^{2} 45 ° = 1$

$R e a s o n (R) : {c s c}^{2} θ - {c o t}^{2} θ = 1 for all values of θ .$

1 Both A and R are true, and R is the correct explanation of A

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false

4 A is false, but R is true

Ans.
(3)

Assertion (A) is true, but Reason (R) is false as the identity ${c s c}^{2} θ - {c o t}^{2} θ = 1 i s n o t d e f i n e d f o r θ = 0 ° .$

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Solution

Q. Assertion(A): csc 245°-cot 245°=1 Reason(R): csc 2θ-cot 2θ=1 for all values of θ.

1 Both A and R are true, and R is the correct explanation of A

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false

4 A is false, but R is true

Ans. (3) Assertion (A) is true, but Reason (R) is false as the identity csc 2θ-cot 2θ=1 is not defined for θ = 0°.

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Q.
$A s s e r t i o n (A) : {c s c}^{2} 45 ° - {c o t}^{2} 45 ° = 1$

$R e a s o n (R) : {c s c}^{2} θ - {c o t}^{2} θ = 1 for all values of θ .$

Ans.
(3)

Assertion (A) is true, but Reason (R) is false as the identity ${c s c}^{2} θ - {c o t}^{2} θ = 1 i s n o t d e f i n e d f o r θ = 0 ° .$