Plzzz help class 9 optional math

If tan theta =p show that sec theta*cosec theta =p+1/p

Step-by-step explanation:

The given trigonometric relations are

tan(θ) = p

sec(θ)×cosec(θ) = p + 1/p

We note that, when tan(θ) = p, we have;

p + 1/p = tan(θ) + 1/(tan(θ)) = (tan²(θ) + 1)/tan(θ)

By trigonometric ratios, we have;

tan²(θ) + 1 = sec²(θ) =1/cos²(θ) which gives;

(tan²(θ) + 1)/tan(θ) = 1/cos²(θ) × 1/tan(θ)  = cos(θ)/sin(θ)×1/cos²(θ)  

Therefore;

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