Question

if tan theta is equals to 1 then find the values of sin theta + cos theta upon sec theta + cosec theta

Answer 1

The value of (Sin θ + Cos θ)/ (Sec θ + Cosec θ) is 1/2

Given:

Tan θ = 1  

To find:

(Sin θ + Cos θ)/ (Sec θ + Cosec θ)

Solution:

Formulas used:

From the Trigonometric ratio table

=>  Tan 45° = 1  

=>  Sin 45° = 1/√2      

=>  Cos 45° = 1/√2  

=>  Sec 45° = √2  

=>  Cosec 45° = √2

Given Tan θ = 1    

As we know Tan 45° = 1  

=> Tan θ = Tan 45°  

=>  θ = 45°    

(Sin θ + Cos θ)/ (Sec θ + Cosec θ)  

= (Sin 45° + Cos 45°)/ (Sec 45° + Cosec 45°)  

= (1/√2 + 1/√2)/ (√2 + √2)

= $\frac{2}{ \sqrt{2} } \times \frac{1}{2 \sqrt{2} }$      

= 1/2

Therefore,

The value of (Sin θ + Cos θ)/ (Sec θ + Cosec θ) is 1/2  

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