Trigonometric Identities
ICSE · Class 10 · Mathematics
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If sin θ = 3/5, find the value of cos θ.
If tan θ = 4/3, find sec θ.
The value of sin²30° + cos²30° is:
If cosec θ = 13/5, find cot θ.
Sample Questions
Which of the following are equivalent to sec²θ?
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1 + tan²θ, 1/cos²θ, cosec²θ - cot²θ
From the identity 1 + tan²θ = sec²θ. Also, sec θ = 1/cos θ, so sec²θ = 1/cos²θ. Using cosec²θ = 1 + cot²θ and sec²θ cosec²θ = 1, we get cosec²θ - cot²θ = sec²θ.
Which identity is correct?
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1 + cot²θ = cosec²θ
This is one of the three fundamental trigonometric identities. The other two are sin²θ + cos²θ = 1 and 1 + tan²θ = sec²θ.
If sin θ = 5/13, find tan θ.
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5/12
First find cos θ using sin²θ + cos²θ = 1. cos²θ = 1 - (5/13)² = 1 - 25/169 = 144/169. So cos θ = 12/13. Then tan θ = sin θ/cos θ = (5/13)/(12/13) = 5/12.
The expression (sec²θ - 1) is equal to:
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tan²θ
From the identity 1 + tan²θ = sec²θ, we can rearrange to get sec²θ - 1 = tan²θ.
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