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Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

Assertion The value of each of the trigonometric ratios of an angle does not depend on the size of the triangle. It only depends on the angle.

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

A) A is true, R is true; R is a correct explanation for A.

B) A is true, R is true; R is not a correct explanation for A.

C) A is true; R is false.

D) A is false; R is true.

Correct Answer: B

Solution :

In \[\Delta ABC\] and in \[\Delta PQR\]

\[\sin \,C=\frac{AB}{AC}\] And  \[\operatorname{sinR}=\frac{6}{10}\]

\[\Rightarrow \,\,\sin C=\frac{3}{5}\]

\[\Rightarrow \,\,\,\sin R=\frac{3}{5}\]

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

Assertion is True and Reason is True but Reason is not the correct explanation of Assertion+.