Question

If cosec theta minus sin theta is equals to M cube and secant theta minus cos theta = 2 and cube then prove that and raise to power 4 and square + sin square x by 4 is equals to 1​

Answer 1

CORRECT QUESTION :

If cosec theta - sin theta=m³ and sec theta - cos theta=n³, then prove that (m^2n)^2/3 + (mn^2)^2/3 = 1

cosec Ф - sin Ф = m³ .

⇒ 1/sin Ф - sin Ф = m³

⇒ ( 1 - sin²Ф )/sin Ф = m³

⇒ cos²Ф/sin Ф = m³

⇒ cot Ф  cos Ф = m³

⇒ cos²Ф / sin Ф = m³ .........( 1 )

sec Ф - cos Ф = n³

⇒ 1/cosФ - cosФ = n³

⇒ ( 1 - cos²Ф )/cosФ = n³

⇒ sin²Ф/cosФ = n³ ...........( 2 )

We have to prove that :

(m²n)^2/3 + (mn²)^2/3 = 1

⇒ ( cos⁴Ф/sin²Ф . sin²Ф/cosФ )^(2/3) + ( sin⁴Ф/cos²Ф . cos²Ф/sinФ)^(2/3)

= cos²Ф + sin²Ф

= 1

Hence proved !

Answer 2

Answer:

Answer:ANSWER IS GIVEN IN ATTACHMENT BELOW