Two Brackets, One Neat Product
Prove that (sec θ − cos θ)(cot θ + tan θ) = tan θ sec θ, one bracket at a time.
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Trigonometry Prove That questions, Class 10
Watching someone else prove an identity is easy. Doing it yourself is the hard part. Here are three new proofs to try, each split into the small decisions you would make on paper.
Three proofs to try
The Hidden Partner Expression
If 5 sin θ + 12 cos θ = 13, prove that tan θ = 5/12 without finding θ.
Try it step by stepTwo Fractions That Collapse
For an acute angle θ, prove that tan²θ/(sec θ − 1) + cot²θ/(cosec θ + 1) = sec θ + cosec θ.
Try it step by stepEach question is split into small steps. If you get stuck, the hints ask you a question that points the way. They never just show you the answer. Every question was written for Young Math Brains and checked twice.
How to start any Prove That question
- Work on one side only, usually the more complicated one, and change it until it becomes the other side.
- When you are stuck, write every ratio in terms of sin θ and cos θ.
- Look for the three identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ. A square next to a 1 is often one of them in disguise.
- Combine fractions into one fraction before you cancel anything.
- If you are given a condition such as 5 sin θ + 12 cos θ = 13, ask which partner expression would cancel the cross term when you square.
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