CAIE IGCSE Additional Math 10.6 Prove Trigonometric Relationships QuestionsPractise Cambridge IGCSE Additional Mathematics by proving trigonometric identities through sine-cosine rewrites and valid simplification.Syllabus2028–2030CourseAdditional Mathematics 0606
Exam pointsProve trigonometric identities by rewriting ratios in sine and cosine.Apply reciprocal, quotient and Pythagorean identities to simplify both sides.Track domain restrictions and present a complete algebraic proof of equivalence.
CAIE IGCSE Additional Math 10.6 Prove Trigonometric Relationships Questions question 1[Maximum number: 3]Show that 1−sinxcosx+cosx1−sinx=2secx\frac{1-\sin x}{\cos x}+\frac{\cos x}{1-\sin x}=2 \sec xcosx1−sinx+1−sinxcosx=2secx.Mark as masteredShow Answer(1−sinx)2+cos2xcosx(1−sinx)or1−2sinx+sin2x+cos2xcosx(1−sinx) oe\begin{aligned} \frac{(1-\sin x)^2+\cos^2 x}{\cos x(1-\sin x)} &\quad\text{or}\quad \frac{1-2\sin x+\sin^2 x+\cos^2 x}{\cos x(1-\sin x)}\ \text{oe} \end{aligned}cosx(1−sinx)(1−sinx)2+cos2xorcosx(1−sinx)1−2sinx+sin2x+cos2x oeM1 common denominator.2−2sinxcosx(1−sinx)\frac{2-2\sin x}{\cos x(1-\sin x)}cosx(1−sinx)2−2sinx oeA1 for use of cos2x+sin2x=1\cos^2 x+\sin^2 x=1cos2x+sin2x=1.2(1−sinx)cosx(1−sinx)\frac{2(1-\sin x)}{\cos x(1-\sin x)}cosx(1−sinx)2(1−sinx), with correct completion to 2secx2\sec x2secxA1 fully justified with sufficient detail.Add to Test