Question

Help me with this trigonometric sum.....I have exam.......I will award brainliest

Answer 1

Hey there...❗
Here is ur answer..


➡⏩Plz refer to the attachment⏪⬅

Hope it will help.☺
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Answer 2

Given Equation is (x/a) cos Ф + (y/b) sin Ф = 1.

On squaring both sides, we get

⇒ (x/a cos Ф + y/b sin Ф)^2 = (1)^2

⇒ (x^2/a^2) cos^2 Ф + (y^2/b^2) sin^2 Ф + (2xy/ab) cos Ф sin Ф = 1  -- (1)

Given Equation is (x/a) sin Ф - (y/b) cos Ф = 1.

On Squaring both sides, we get

⇒ (x/a sin Ф - y/b cos Ф)^2 = (1)^2

⇒ (x^2/a^2) sin^2 Ф + (y^2/b^2) cos^2 Ф - (2xy/ab) sin Ф cos Ф = 1  -- (2)

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On solving (1) & (2), we get

⇒ (x^2/a^2) cos^2 Ф + (y^2/b^2) sin^2 Ф + (x^2/a^2) sin^2 Ф + (y^2/b^2) cos^2 Ф = 2

⇒ x^2/a^2(cos^2 Ф + sin^2 Ф) + y^2/b^2(sin^2 Ф + cos^2 Ф) = 2

⇒ (x^2/a^2) + (y^2/b^2) = 2.

Hope it helps!