Question

plz ans tignometry class 12th​

Answer 1

Answer:

(A) T₁ / T₃

Step-by-step explanation:

First, get to know what the expressions in the numerator and denominator look like.  The both take the form

 Tₙ₊₂ - Tₙ

= sinⁿ⁺² θ + cosⁿ⁺² θ - sinⁿ θ - cosⁿ θ

= sinⁿ θ ( sin² θ - 1 ) + cosⁿ θ ( cos² θ - 1 )

= sinⁿ θ ( -cos² θ ) + cosⁿ θ ( -sin² θ )

= -sin² θ cos² θ ( sinⁿ⁻² θ + cosⁿ⁻² θ )

= -sin² θ cos² θ Tₙ₋₂

Now we use this for the numerator (n=3) and the denominator (n=5), cancelling out the -sin²θ cos²θ in each, to get

( T₅ - T₃ ) / ( T₇ - T₅ ) = T₁ / T₃

Hope this helps