Q5 of 186 Page 343

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

Given: (cosec θ + cot θ) = m …………….(1)

(cosec θ – cot θ) = n …………….(2)

Multiply equation (1) and (2):

(cosec θ + cot θ) (cosec θ – cot θ) = mn

(cosec² θ – cot² θ) = mn

1 = mn (∵ 1 + cot² θ = cosec² θ)

Therefore, mn = 1.

Hence, proved.

If prove that

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

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

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