LIVE Course for free

Rated by 1 million+ students
Get app now
Class 8 Foundation Course
Class 9 Foundation Course
Class 10 Foundation Course
Class 11 Foundation Course
Class 12 Foundation Course
JEE COURSE
NEET COURSE
0 votes
19 views
in Trigonometry by (30.0k points)
closed by

What is (1 + cot θ - cosec θ)(1 + tan θ + sec θ) equal to?


1. 1
2. 2
3. 3
4. 4

1 Answer

0 votes
by (54.3k points)
selected by
 
Best answer
Correct Answer - Option 2 : 2

Concept:

Trigonometry Formula

cot θ = \(\rm \frac{cos θ }{sin θ }\)

tan θ = \(\rm \frac{sin θ }{cos θ }\)

cosec θ = \(\rm \frac{1 }{sin θ }\)

sec θ = \(\rm \frac{1}{cos θ }\)

sin2 θ + cos2 θ = 1

(sin θ + cos θ)2 = sin2 θ + cos2 θ + 2 sin θ cos θ 

 

Calculation:

To Find: Value of (1 + cot θ - cosec θ)(1 + tan θ + sec θ)

= (1 + \(\rm \frac{cos θ }{sin θ }\) - \(\rm \frac{1 }{sin θ }\)) (1 + \(\rm \frac{sin θ }{cos θ }\) + \(\rm \frac{1}{cos θ }\))

\(\rm \frac{(sin θ + cos θ - 1) ( sin θ + cos θ + 1)}{sin θ \: cosθ }\)

\(\rm \frac{( sin θ + cos θ )^{2} - 1}{ sin θ cos θ }\)

\(\rm \frac{sin^{2}θ + cos^{2}θ + 2 sin θ cos θ - 1}{sinθ \: cos θ }\)

\(\rm \frac{1 + 2 sin θ cos θ - 1}{sinθ \: cos θ }\)

\(\rm \frac{2 sin θ cos θ }{sinθ \: cos θ }\)

= 2

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

...