Question

sintheta+ costheta/
Sintheta-costheta=3/2

then the value
of
tantheta = ?​

Answer 1

Answer:

If sinθ+cosθ=  

2

​  

, then find the value of tanθ+cotθ.

Study later

ANSWER

Consider the given equation,

sinθ+cosθ=  

2

​  

      …(1)

Taking square both sides,

 sin  

2

θ+cos  

2

θ+2sinθcosθ=2

1+2sinθcosθ=2

2sinθcosθ=1

sinθcosθ=  

2

1

​  

       ……(2)

Now, divided by cosθ in equation 1st , we get

tanθ+1=  

cosθ

2

​  

 

​  

      ….(3)

Again divided by sinθ in equation 1st, we get

1+cotθ=  

sinθ

2

​  

 

​  

           ….(4)

Add equation 1st and 2nd , we get

tanθ+cotθ+2=  

cosθ

2

​  

 

​  

+  

sinθ

2

​  

 

​  

 

tanθ+cotθ=  

2

​  

.(  

sinθcosθ

sinθ+cosθ

​  

)−2        ……(5)

Now, from equation 1st ,2nd and 5th ,we get

 tanθ+cotθ=  

2

​  

.  

⎝

⎜

⎜

⎛

​  

 

2

1

​  

 

2

​  

 

​  

 

⎠

⎟

⎟

⎞

​  

−2

tanθ+cotθ=2

Hence, this is the answer.

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