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

0 votes
19 views

closed

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

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

0 votes
1 answer
0 votes
1 answer
0 votes
1 answer
0 votes
1 answer
0 votes
1 answer