Assertion (A): The value of \frac{{cos{\ }}^2\theta}{{sin{\ }}^2\theta}-\frac{1}{{sin{\ }}^2\theta} is 1. Reason (R): {sin{\ }}^2\theta+{cos{\ }}^2\theta

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

Q.
Assertion (A): The value $o f \frac{{c o s}^{2} θ}{{s i n}^{2} θ} - \frac{1}{{s i n}^{2} θ} i s 1 .$

Reason (R): ${s i n}^{2} θ + {c o s}^{2} θ = 1,$ for any value of $θ$ , for which trigonometric ratios involved in it are defined.

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.
(4)

$F o r a s s e r t i o n (A), w e h a v e, \frac{{c o s}^{2} θ}{{s i n}^{2} θ} - \frac{1}{{s i n}^{2} θ} = \frac{{c o s}^{2} θ - 1}{{s i n}^{2} θ} = \frac{- (1 - {c o s}^{2} θ)}{{s i n}^{2} θ} = \frac{- {s i n}^{2} θ}{{s i n}^{2} θ} = - 1 [∵ {c o s}^{2} θ + {s i n}^{2} θ = 1 \Rightarrow {s i n}^{2} θ = 1 - {c o s}^{2} θ]$

Hence, assertion (A) is false.

Also, fact given under reason (R) is well-known identity. So, it is true.

Solution

Q.
Assertion (A): The value $o f \frac{{c o s}^{2} θ}{{s i n}^{2} θ} - \frac{1}{{s i n}^{2} θ} i s 1 .$

Reason (R): ${s i n}^{2} θ + {c o s}^{2} θ = 1,$ for any value of $θ$ , for which trigonometric ratios involved in it are defined.

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.

Want Us to Email you About Special Offers & Updates?

Solution

Q. Assertion (A): The value of cos 2θsin 2θ-1sin 2θ is 1. Reason (R): sin 2θ+cos 2θ=1,for any value of θ, for which trigonometric ratios involved in it are defined.

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. (4) For assertion (A),we have,cos 2θsin 2θ-1sin 2θ=cos 2θ-1sin 2θ=-1-cos 2θsin 2θ=-sin 2θsin 2θ=-1∵cos 2θ+sin 2θ=1⇒sin 2θ=1-cos 2θ Hence, assertion (A) is false. Also, fact given under reason (R) is well-known identity. So, it is true.

Want Us to Email you About Special Offers & Updates?

Q.
Assertion (A): The value $o f \frac{{c o s}^{2} θ}{{s i n}^{2} θ} - \frac{1}{{s i n}^{2} θ} i s 1 .$

Reason (R): ${s i n}^{2} θ + {c o s}^{2} θ = 1,$ for any value of $θ$ , for which trigonometric ratios involved in it are defined.