Question

if 7cosecA-3cot=7 then prove that 7cot-3 cotA=3​

Answer 1

Answer:

The given equation is, 7 cosec θ − 3 cot θ = 7squaring both sides, we get (7 cosec θ − 3 cot θ)2 = 49

⇒(7cosec θ)2 + (3cot θ)2 − 2(7cosec θ)(3cot θ) = 49

⇒49 cosec2θ + 9cot2θ − 42 cosec θ cot θ = 49

⇒49(1 + cot2θ) + 9(cosec2θ − 1) − 42 cosec θ cot θ = 49

⇒49 + 49cot2θ + 9cosec2θ − 9 − 42 cosec θ cot θ = 49

⇒ 49cot2θ + 9cosec2θ − 42 cosec θ cot θ = 9

⇒(7cot θ)2 + (3cosec θ)2 − 2(7cot θ)(3cosec θ) = 9

⇒(7 cot θ − 3 cosec θ)2 = 9

⇒(7 cot θ − 3 cosec θ) = 3

Step-by-step explanation:

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