LIVE Course for free

Rated by 1 million+ students
Get app now
JEE MAIN 2023
JEE MAIN 2023 TEST SERIES
NEET 2023 TEST SERIES
NEET 2023
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
67 views
in Trigonometry by (30.0k points)
closed by
If sin θ × cos θ = √3/4, then sin4 θ + cos4 θ is equal to :-
1. 5/8
2. 5/2
3. 3/2
4. 4/5

1 Answer

0 votes
by (41.6k points)
selected by
 
Best answer
Correct Answer - Option 1 : 5/8

Given:

sin θ × cos θ = √3/4,

Formula used:

sin2 θ + cos2 θ = 1

(a + b)2 = a2 + b2 + 2ab

⇒ (a + b)2 – 2ab = a2 + b2

Calculation:

sin4 θ + cos4 θ

⇒ (sinθ)2 + (cos2 θ)2 = [(sinθ) + (cos2 θ)]2 – 2(sinθ)(cos2 θ)

⇒ [1 – 2(sinθ)(cos2 θ)]

⇒ [1 – 2{(sin θ)(cos θ)}2]

⇒ [1 – 2 × (√3/4)2]

⇒ [1 – 2 × (3/16)]

⇒ (1 – 3/8)

⇒ (8 – 3)/8

⇒ 5/8

∴ The answer is 5/8.

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

...