Question

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Answer 1

Explanation:

A >

Divide both side by sin^2 x , and we get

Subtracting cosec^2 x from both sides we get

B>lets break tan θ into its components tan θ = sin θ / cos θ and cot θ = 1/ tan θ

Tan θ + cot θ= Sin θ/cos θ + cos θ/ sin θ = sin^2 θ + cos^2 θ / sin θ cos θ= 1/ sin θ cos θ = sec θ cosec θ

Answer 2

See below

Explanation:

A >
`Sin^(2) x + cos^(2) x = 1 \\`

Divide both side by sin^2 x , and we get

`(sin^2 x)/(sin^2 x) + (cos^2 x)/( sin^2 x) = (1)/(sin^2 x)`

`1+ cot^2 x= cosec^2 x`

Subtracting cosec^2 x from both sides we get

`Cosec^2 x - cot^2 x = 1`

B>lets break tan θ into its components tan θ = sin θ / cos θ and cot θ = 1/ tan θ

Tan θ + cot θ= Sin θ/cos θ + cos θ/ sin θ = sin^2 θ + cos^2 θ / sin θ cos θ= 1/ sin θ cos θ = sec θ cosec θ