1. Which of the following is equal to the trigonometric identity, sin(x) * sec(x)?
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Correct answer is option - 3
Explanation:
To simplify sin(x) * sec(x), we can re-write sec(x) as 1/cos(x).
This gives, sin(x) * sec(x) = sin(x) * 1/cos(x) ==> sin(x)/ cos(x) = tan(x).
2. Which of the following is equal to the trigonometric identity, sec(x) * cot(x)?
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Correct answer is option - 1
Explanation:
To simplify sec(x) * cot(x), we can re-write sec(x) as 1/cos(x) and cot(x) as cos(x)/sin(x).
This gives, sec(x) * cot(x) = [1/cos(x)] * [cos(x)/sin(x)] ==>1/sin(x) = cosec(x).
3. The simplified form of the trigonometric expression tan(x) + cot(x) is?
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Correct answer is option - 2
Explanation: tan(x) + cot(x) = [sin(x)/ cos(x)] + [cos(x)/ sin(x)].
Taking a common denominator gives: [sin^{2}(x) + cos^{2}(x)]/ [sin(x) * cos(x)]
According to a trigonometric identity, sin^{2}(x) + cos^{2}(x) = 1.
Hence, we get: 1/ [sin(x) * cos(x)] -> cosec(x) * sec(x).
4. Which is the simplified form of (sin(x) + cos(x))^{2}?
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Correct answer is option - 3
Explanation: (sin(x) + cos(x))^{2} is in the form of (a + b)^{2} where we can expand it as a^{2} + 2ab + b^{2}.
This gives: (sin(x) + cos(x))^{2} = sin^{2}(x) + 2sin(x)cos(x) + cos^{2}(x).
Since sin^{2}(x) + cos^{2}(x) = 1,
Hence we get: sin^{2}(x) + 2sin(x) cos(x) + cos^{2}(x) ->1 + 2sin(x) cos(x).
5. Which of the following is equal to the trigonometric identity, tan(x) /sin(x)?
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Correct answer is option - 4
Explanation: To simplify tan(x) /sin(x), we can re-write tan(x) as sin(x)/cos(x).
This gives, tan(x) /sin(x) = [sin(x)/cos(x)] / sin(x) -> 1/cos(x) = sec(x).