Question

ayuda
tan²θ -1/sen θ +cosθ = senθ-cosθ/cos²θ ​

Answer 1

Respuesta: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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