Question

If tan theta equals to 1 find the value of sin theta + cos theta

Answer 1

Solution :

Given,

tan∅ = 1

To finD

sin∅ + cos∅

Consider the relation tan∅ = 1.

$\sf \: \tan( \theta) = 1 \\ \\ \longrightarrow \: \sf \: tan \theta= tan45 \\ \\ \longrightarrow \: \sf \: \theta = 45^{\circ}$

The angle is 45°

Now,

$\sf \: \sin(45) + \cos(45) \\ \\ \implies \: \sf \: \dfrac{1}{ \sqrt{2} } + \dfrac{1}{ \sqrt{2} } \\ \\ \implies \: \sf \: \dfrac{2}{ \sqrt{2} } \implies \: \sqrt{2}$

Thus,sin∅ + cos∅ = √2

Also,

Tan∅ = 1

→ Tan45 = tan∅

→ tan∅ = tan(180 + 45)

→ tan∅ = tan225

→ ∅ = 225°

Now,

(180 + ∅) lies in third quadrant,cos and sin would be negative

So,

sin225 + cos225

= - 1/√2 - 1/√2

= - √2

Thus,sin∅ + cos∅ = ± √2