Question

1+ tan square tetha=?
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Answer 1

Answer:

1+10^2 ....i didn't know the value of theta yrr.... s

so I can't do it....

I hope you can understand

because I am in class 9th only....

and teachers were not taugh... so

kindly plzz understand

Answer 2

Answer:

1 + Tan²θ = Sec²θ

Step-by-step explanation:

TO PROVE: 1 + Tan²θ = Sec²θ

Tan θ = (Sin θ) / (Cos θ)

∴ Tan²θ = (Sin θ / Cos θ)²  .. (1)

L.H.S = 1 + Tan²θ

(substituting from equation 1 we get)

L.H.S. = 1 + (sin θ/cos θ)²

∴ L.H.S = 1 + (Sin²θ / Cos²θ)

∴ L.H.S. = (Cos²θ + Sin²θ) / Cos²θ

But, we know that - Cos²θ + Sin²θ = 1

∴ L.H.S. = 1 / Cos²θ

  ∵ 1 / Cosθ = Secθ

∴ L.H.S. = Sec²θ = R.H.S.

as LHS = RHS... hence proved

1 + Tan²θ = Sec²θ

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