Trigonometry · Guided Practice

Trig Identities

10 questions with answers and video solutions. Try each one before revealing the answer.

1
2016 P1 Q11
2 Marks

Simplify tan⁡2x∘cos⁡2x∘\displaystyle \tan^{2}x^{\circ}\cos^{2}x^{\circ}.

2
2018 P1 Q18
2 Marks

Express sin⁡x∘cos⁡x∘tan⁡x∘\displaystyle \sin x^{\circ}\cos x^{\circ}\tan x^{\circ} in its simplest form.
Show your working.

3
2019 P2 Q17
2 Marks

Expand and simplify (sin⁡x∘+cos⁡x∘)2.\displaystyle (\sin x^{\circ}+\cos x^{\circ})^{2}.
Show your working.

4
2021 P2 Q16

Expand and simplify cos x∘(tan x∘+1).\displaystyle cos\ x^\circ (tan\ x^\circ +1).

Show your working.

No hints on this one — its full written solution is with the answer.

5
2022 P2 Q13
2 Marks

Simplify sin⁡x∘+2cos⁡x∘cos⁡x∘\displaystyle \frac{\sin x^{\circ}+2\cos x^{\circ}}{\cos x^{\circ}}.

6
2023 P2 Q13
2 Marks

Simplify 2sin⁡2x∘+2cos⁡2x∘\displaystyle 2\sin^2 x^\circ + 2\cos^2 x^\circ Show your working.

7
2024 P2 Q16
2 Marks

Express 3cos⁡2x∘−1\displaystyle 3\cos^2 x^{\circ} - 1 in the form a+bsin⁡2x∘.\displaystyle a + b \sin^2 x^{\circ}.
Show your working.

8
Solve the equation 3 sin x=2 cos x\displaystyle 3\ sin\ x = 2\ cos\ x, for 0≤x<360∘.\displaystyle 0 \le x < 360^\circ.

No hints on this one — its full written solution is with the answer.

9
Prove that, for all values of x∘\displaystyle x^\circ, cos2x(1+tan2x)=1.\displaystyle cos^2 x(1+tan^2 x)=1.
Video solution coming soon

No hints on this one — its full written solution is with the answer.

10
2026 P2 Q9
3 Marks
Express
x2−815÷x+92\displaystyle \frac{x^{2}-81}{5}\div\frac{x+9}{2}, x≠−9\displaystyle x\ne-9
as a single fraction in its simplest form.

Keep practising

More trig identities questions

New questions, modelled on past paper questions and checked against their marking instructions. Not reprints — you have not seen these before.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.

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