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Mathematics · JEE

Trigonometry Short Tricks for JEE

42+ syllabus-aligned questions available

Quick answer

Short tricks for Trigonometry work only with strong fundamentals. Apply the tips below in timed sets and review every explanation.

Use these Trigonometry shortcuts to save time in JEE Mathematics papers — then validate speed with 42+ MCQs on Goodmarks.

Short tricks for speed

  • Trigonometry focus drill

    Solve 15 mixed MCQs for Trigonometry, review every explanation, and note formulas you hesitated on.

  • Calculus substitution scan

    Spot standard forms (sin²x, 1/(a²+x²), e^ax) before integrating — JEE rewards pattern recognition.

  • Graph sketch shortcut

    For coordinate geometry, mark intercepts and asymptotes first; many MCQs need only qualitative graph features.

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Q1MathsUnit 14: Trigonometry
Assertion Consider f(x)=sin⁡−1(sec⁡(tan⁡−1x)+\boldsymbol{f}(\boldsymbol{x})=\sin ^{-1}\left(\sec \left(\tan ^{-1} \boldsymbol{x}\right)+\right. cos⁡−1(cosec⁡(cot⁡−1x)\cos ^{-1}\left(\operatorname{cosec}\left(\cot ^{-1} x\right)\right. Statement-1: Domain of f(x)f(x) is a singleton. Reason Statement-2: Range of the function f(x)\boldsymbol{f}(\boldsymbol{x}) is a singleton.
Q2MathsUnit 14: Trigonometry
The number of real solutions of the equation tan⁡−1x(x+1)+\tan ^{-1} \sqrt{x(x+1)}+ sin⁡−1x2+x+1=π2\sin ^{-1} \sqrt{x^{2}+x+1}=\frac{\pi}{2} is
Q3MathsUnit 14: Trigonometry
A=cos⁡200cos⁡400cos⁡600cos⁡800\mathbf{A}=\cos 20^{0} \cos 40^{0} \cos 60^{0} \cos 80^{0} B=cos⁡60cos⁡420cos⁡660cos⁡780\mathbf{B}=\cos 6^{0} \cos 42^{0} \cos 66^{0} \cos 78^{0} C=cos⁡360cos⁡720cos⁡1080cos⁡1440\mathbf{C}=\cos \mathbf{3} \mathbf{6}^{\mathbf{0}} \cos \mathbf{7} \mathbf{2}^{\mathbf{0}} \cos \mathbf{1 0} \mathbf{8}^{\mathbf{0}} \cos \mathbf{1} \mathbf{4} \mathbf{4}^{\mathbf{0}}
Q4MathsUnit 14: Trigonometry
The measures of the angles of a triangle are in the ratio 4:5:9.4: 5: 9 . The triangle is:
Q5MathsUnit 14: Trigonometry
If value of x\mathbf{x} which satisfy equation (cot⁡−1x)2−3(cot⁡−1x)+2>0\left(\cot ^{-1} x\right)^{2}-3\left(\cot ^{-1} x\right)+2>0 is x<x< cot⁡a\cot a or x>cot⁡bx>\cot b Find the value of a+ba+b
Q6MathsUnit 14: Trigonometry
ln⁡ΔABC,BC=AB\ln \Delta A B C, B C=A B and ∠B=80∘\angle B=80^{\circ} Then ∠A\angle A is equal to
Q7MathsUnit 14: Trigonometry
Two line segments ABA B and ACA C include an angle of 60060^{0} where AB=5cmA B=5 \mathrm{cm} and ACA C =7cm.=7 \mathrm{cm} . Locate points P\mathrm{P} and Q\mathrm{Q} on AB\mathrm{AB} and AC,A C, respectively such that AP=34A P=\frac{3}{4} ABA B and AQ=14AC.A Q=\frac{1}{4} A C . Join PP and QQ and measure the length PQ.
Q8MathsUnit 14: Trigonometry
Statement I: The equation (sin⁡−1x)3+(cos⁡−1x)3−aπ3=0\left(\sin ^{-1} x\right)^{3}+\left(\cos ^{-1} x\right)^{3}-a \pi^{3}=0 has solution for all a⩾132a \geqslant \frac{1}{32} Statement II : For any xϵR,sin−1x+\boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}, \boldsymbol{s} \boldsymbol{i n}^{-1} \boldsymbol{x}+ cos⁡−1x=π2\cos ^{-1} x=\frac{\pi}{2} and 0≤(sin⁡−1x−π4)2≤0 \leq\left(\sin ^{-1} x-\frac{\pi}{4}\right)^{2} \leq 9π216\frac{9 \pi^{2}}{16}

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Frequently asked questions

Are short tricks enough for Trigonometry in JEE?

No — tricks complement concepts. Master the theory first, then use shortcuts in timed MCQ practice.

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