please give me answer of maths question 5
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EXPLANATION.
⇒ [cosec(A) - sin(A)].[sec(A) - cos(A)] = 1/tan(A) + cot(A).
As we know that,
From L.H.S, we get.
⇒ [cosec(A) - sin(A)].[sec(A) - cos(A)].
⇒ [1/sin(A) - sin(A)].[1/cos(A) - cos(A)].
⇒ [1 - sin²A/sin(A)].[1 - cos²A/cos(A)].
⇒ [cos²A/sin(A)].[sin²A/cos(A)].
⇒ [cos²A/sin(A) x sin²A/cos(A)].
⇒ [cos(A).sin(A)].
From R.H.S, we get.
⇒ 1/tan(A) + cot(A).
⇒ 1/[sin(A)/cos(A)] + [cos(A)/sin(A)].
⇒ 1/sin²A + cos²A/cos(A).sin(A).
⇒ 1/1/cos(A).sin(A).
⇒ 1/1 x cos(A).sin(A)/1.
⇒ cos(A).sin(A).
Hence Proved.
MORE INFORMATION.
(1) = sin²x + cos²x = 1.
(2) = 1 + tan²x = sec²x.
(3) = 1 + cot²x = cosec²x.
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