Question

44. If cosec - sin 0 = mº and sec 0 - cos 8 = n then prove that m'n? + m n = 1​

Answer 1

Answer:

Given cosec theta - sin theta = m, sec theta - cos theta = n

Given that cosec theta - sin theta = m

→ !/sin theta - sin theta = m

⇒ (1-sin² theta)/sin theta = m → cos² theta/sin theta = m

and sec theta - cos theta = n

⇒ 1/cos theta - cos theta = n → (1-cos² theta)/cos theta = n

sin² theta/cos theta = n

Now (m²n)²/³ + (mn²)²/³

⇒ (cos⁴ theta/sin² theta × sin² theta/cos theta)²/³ + (cos² theta/sin theta × sin⁴ theta/cos² theta)²/³

⇒ (cos³ theta)²/³ + (sin³ theta)²/³

⇒cos² theta + sin² theta

= 1 Hence proved

Step-by-step explanation:

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