Pls solve question no. 3

Pls solve question no. 3 21(E) If x a cos O and y b cot O, show that 4. If sec A + tan A p. show that 2 -1 If tan A = n tan B and sin A = m stn B, m2 — I (i) If 2 sin A — I 0. show that Sin 3A z 3 Sin A- 4 sin8 A ill) If 4 cos2 A 3 z 0, show that cos 3 A 4 coO A — 3 cosA

Dear Student,

Answer 3:

x = a \cos θ \Rightarrow x^{2} = {(a \cos θ)}^{2} = a^{2} \cos^{2} θ y = b c o t θ \Rightarrow y^{2} = (b c o t θ) = b^{2} co t^{2} θ \frac{a^{2}}{x^{2}} - \frac{b^{2}}{y^{2}} = \frac{a^{2}}{a^{2} \cos^{2} θ} - \frac{b^{2}}{b^{2} co t^{2} θ} = \frac{1}{\cos^{2} θ} - \frac{1}{co t^{2} θ} = s e c^{2} θ - \tan^{2} θ {S i n c e \frac{1}{\cos θ} = s e c θ a n d \frac{1}{c o t θ} = \tan θ} = 1 {S i n c e, s e c^{2} x - \tan^{2} x = 1} H e n c e p r o v e d

Regards