Question

If sin theta + cos theta =root 2 then evaluate : tan theta + cot theta

Answer 1

Hello! dear,

Your answer goes like this ...

Given that:-sin theta+cos theta=root 2

                 We have to find tan theta+cot theta=?

                Solution:---

Sin θ+cos θ=√2
Now we have to Square on both sides
={sin θ+cos θ}²=√2²
={sin² θ+cos ² θ}+2 sin θ cos  θ=2
=1+sin θ cos θ=2
⇒sin θ cos θ=1/2


Now,

Tan θ+cot θ=sin θ/cos θ+cos θ/sin θ
={sin² θ+cos² θ} /sin θ cos θ
=1/ {1/2} = 2

Hence,the answer is "2".

Thank you dear,

Hope It helps.

Answer 2

Answer:

Here is a solution along with calculations:

Step-by-step explanation:

Given: sin theta + cos theta = $\sqrt{2}$

To find: Tan Ф + Cot Ф

Here we will calculate,

Sin θ+cos θ=√2

Now we have to put Square on both sides

={sin θ+cos θ}²=√2²

={sin² θ+cos ² θ}+2 sin θ cos  θ=2

=1+sin θ cos θ=2

⇒sin θ cos θ= 1/2

Now,

tanθ + cot θ =sin θ/cos θ + cos θ/sin θ

=( sin² θ +cos² θ) / sin θ cos θ

= 1 / (1/2) = 2 answer

Now, Here we will calculate Tan θ+cot θ,

Tan θ+cot θ=sin θ/cos θ+cos θ/sin θ

={sin² θ+cos² θ} /sin θ cos θ

=1/ {1/2} = 2

Hence the answer is = 2.

• It is a question related to trigonometry.
• Trigonometry is a discipline of mathematics dealing with specific angle functions and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc)

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