Question

If 7 cosec θ =25, find the value of sin θ + cos θ.​

Answer 1

Answer:

31/25

Step-by-step explanation:

Given:

7 cosec θ = 25

To find:

sin θ + cos θ = ?

Solution:

7 cosec θ = 25

⇒ cosec θ = 25 ÷ 7

⇒ Hypotenuse ÷ Opposite side = 25 ÷ 7

So,

• Hypotenuse = 25
• Opposite side = 7

Let us construct a right-angled triangle for this situation.

(Diagram in attachment)

By Pythagoras Theorem,

(AC)² = (AB)² + (BC)²

⇒ 25² = 7² + BC²

⇒ BC² = 25² - 7²

⇒ BC² = 625 - 49

⇒ BC² = 576

⇒ BC = √576

⇒ BC = 24

Now,

sin θ = Opposite side ÷ Hypotenuse

$\Rightarrow \bf{sin \: \theta = \dfrac{7}{25}}$

Finding cos θ:

cos θ = Adjacent side ÷ Hypotenuse

$\Rightarrow \: \bf{cos \: \theta = \dfrac{BC}{AC}=\dfrac{24}{25}}$

sin θ + cos θ

$= \sf{\dfrac{7}{25}+\dfrac{24}{25}}$

$= \sf{\dfrac{31}{25}}$

$\therefore \boxed{\bf{sin \: \theta + cos \: \theta = \dfrac{31}{25}}}$