Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
59 views
in Trigonometry by (239k points)
closed by
If sin θ sec2 θ = 2/3, 0° < θ < 90°, then the value of (tan2 θ + sin2 θ) is:
1. 7/12
2. 13/12
3. 11/12
4. 5/4

1 Answer

0 votes
by (237k points)
selected by
 
Best answer
Correct Answer - Option 1 : 7/12

Given:

sin θ sec2 θ = 2/3

Concept used:

Value putting method.

Calculation:

sinθ × sec2θ = 2/3 where θ° < θ < 90° 

Let us take θ = 30° 

sin30° = 1/2

sec30° = \(\frac{2}{{\sqrt 3 }}\)

sin30° × sec230° = \(\frac{1}{2} × {\left( {\frac{2}{{\sqrt 3 }}} \right)^2}\)

sin30° × sec230° = \(\frac{1}{2} \times \frac{4}{3} = \frac{2}{3}\)

Hence proved.

Now, (tan2θ + sin2θ) = (tan230° + sin230°)

(tan230° + sin230°) = \(\left( {{{\left( {\frac{1}{{\sqrt 3 }}} \right)}^2} + {{\left( {\frac{1}{2}} \right)}^2}} \right)\)

(tan230° + sin230°) = \(\frac{1}{3} + \frac{1}{4}\)

(tan230° + sin230°) = 7/12

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...