Question

If tan teta =24/7find sin teta +cos teta​

Answer 1

Tan theta = opposite / adjacent = 24/7

the other side ( hypotenuse ) = √ 24² + 7² = 25

Sin theta = opposite / hypotenuse = 24/25

cos theta = adjacent / hypotenuse = 7/25

adding both you get 31/25

Answer 2

Hey Pretty Stranger!

Let the Hypotenuse be (x - 1)

Using Pythagoras Theorem :

★ (AC) = (AB)² + (BC)²

→ x² = (24)² + (7)²

→ x² = 576 + 49

→ x² = 625

→ x = 25

Now,

$\sf \: { \sin \theta} = \dfrac{AB}{AC} = \dfrac{24}{25}$

$\sf \: { \cos \theta} = \dfrac{BC}{AC} = \dfrac{7}{25}$

$\star \: \: \sf \sin \theta + \cos \theta = \dfrac{24}{25} + \dfrac{7}{25}$

$\longrightarrow \sf \: \dfrac{24 + 7}{25}$

$\longrightarrow \sf \: \dfrac{ 31}{25}$

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