question_answer

Directions (Q. Nos. 1 - 14): In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:

Assertion (A): The value of each of the trigonometric ratios of an angle do not vary with the lengths of the sides of the triangle, if the angle remains the same.

Reason (R): In right \[\Delta ABC,\] \[\angle B=90{}^\circ \] and \[\angle A=\theta ,\]\[\sin \theta =\frac{BC}{AC}<1\]and \[\cos \theta =\frac{AB}{AC}<1\]as hypotenuse is the longest side.

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 but 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

Correct Answer: B

Solution :

[b]\[\Delta ABC\ \operatorname{and}\ in\ \Delta PQR\]

\[\sin \theta =\frac{AB}{AC}=\frac{3}{5}\ \ and\ \sin \theta =\frac{PQ}{PR}=\frac{6}{10}\]

\[\sin \theta =\frac{3}{5}\ \ and\ \sin \theta =\frac{3}{5}\]

Simllarly, this also holds for other trigonometric ratios

\[\therefore \] Trigonometric ratio does not depend on the size of the triangle.

\[\therefore \] Assertion true : Reason : true but it is not the correct explanation of assertion.