Question

1+cot theta + cosec theta​

Answer 1

Step-by-step explanation:

Solution:

Given,

1 + cot θ = cosec θ

1 + (cos θ/sin θ) = 1/sin θ

(sin θ + cos θ)/sin θ = 1/sin θ

sin θ + cos θ = 1

Squaring on both sides,

(sin θ + cos θ)2 = (1)2

sin2θ + cos2θ + 2 sin θ cos θ = 1

Using the identities sin2A + cos2A = 1 and sin 2A = 2 sin A cos A,

1 + sin 2θ = 1

sin 2θ = 0

sin 2θ = sin 0 = sin π

Therefore, θ = 2nπ + π/2

so it is 2

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Answer 2

Step-by-step explanation:

⇒1+cotθ=cosecθ

⇒1+

sinθ

cosθ

=

sinθ

1

⇒

sinθ

sinθ+cosθ

=

sinθ

1

⇒sinθ+cosθ=1

Squaring both side

⇒(sinθ+cosθ)

2

=1

⇒sin

2

θ+cos

2

θ+2sinθcosθ=1

⇒1+2sinθcosθ=1

⇒sin2θ=0

⇒θ=2nπ+

2

π