CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Value of Standard Angle(30,60,90)

If θ is an ac...

Question

If θ is an acute angle such that $\tan^{2} θ = \frac{8}{7}$ , then the value of $\frac{(1 + \sin θ) (1 - \sin θ)}{(1 + \cos θ) (1 - \cos θ)}$ is

(a) $\frac{7}{8}$
(b) $\frac{8}{7}$
(c) $\frac{7}{4}$
(d) $\frac{64}{49}$

Open in App

Solution

Given that: andis an acute angle

We have to find the following expression

Since

Since

We know thatand

We find:

Hence the correct option is

Suggest Corrections

thumbs-up

3

Similar questions

\cot θ = \frac{15}{8} then evaluate \frac{(1 + \sin θ) (1 - \sin θ)}{(1 + \cos θ) (1 - \cos θ)}

sin θ (1 + tan θ) + c o s θ (1 + cot θ) = csc θ + sec θ

sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + c o s e c θ

cot θ = \frac{7}{8}

then find the value of

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

Q. Prove the following trigonometric identities.

(i)

\sqrt{\frac{\sec θ - 1}{\sec θ + 1}} + \sqrt{\frac{\sec θ + 1}{\sec θ - 1}} = 2 cosec θ

\sqrt{\frac{1 + \sin θ}{1 - \sin θ}} + \sqrt{\frac{1 - \sin θ}{1 + \sin θ}} = 2 \sec θ

\sqrt{\frac{1 + \cos θ}{1 - \cos θ}} + \sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = 2 cosec θ

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

\frac{\sin θ + 1 - \cos θ}{\cos θ - 1 + \sin θ} = \frac{1 + \sin θ}{\cos θ}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Trigonometric Ratios of Standard angle(30,60,90)

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Value of Standard Angle(30,60,90)

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon