If x = a cos3 θ and y = b sin3 θ, prove that

Given: x = a cos3 θy = b sin3 θConsider L.H.S. = = = (cos3 θ)2/3 + (sin3 θ)2/3= (cos2 θ + (sin2 θ)= 1 = R.H.S.Hence, proved.

Q6 of 186 Page 343

If x = a cos³ θ and y = b sin³ θ, prove that

Given: x = a cos³ θ

y = b sin³ θ

Consider L.H.S. =

= (cos³ θ)^2/3 + (sin³ θ)^2/3

= (cos² θ + (sin² θ)

= 1 = R.H.S.

Hence, proved.

If (sec θ + tan θ) = m and (sec θ – tan θ) = n, show that mn = 1.

If (cosec θ + cot θ) = m and (cosec θ – cot θ) = n, show that mn = 1

If (tan θ + sin θ) = m and (tan θ – sin θ) = n, prove that (m² – n²)² = 16mn.

If (cot θ + tan θ) = m and (sec θ – cos θ) = n, prove that (m²n) ^2/3 – (mn²) ^2/3 = 1.