KCET · Maths · Trigonometric Ratios & Identities
\(3(\sin x-\cos x)^{4}+6(\sin x+\cos x)^{2}\)
\(+4\left(\sin ^{6} x+\cos ^{6} x\right)\)
is equal to
- A 12
- B 13
- C 14
- D 11
Answer & Solution
Correct Answer
(B) 13
Step-by-step Solution
Detailed explanation
\(3(\sin x-\cos x)^{4}+6(\sin x+\cos x)^{2}\)
\(+4\left(\sin ^{6} x+\cos ^{6} x\right)\)
\(=3(1-2 \sin x \cos x)^{2}+6(1+2 \sin x \cos x)\)
\(\quad+4\left(\sin ^{2} x+\cos ^{2} x\right)\left(\sin ^{4} x+\cos ^{4} x\right.\)
\(\left.\quad-\sin ^{2} x \cos ^{2} x\right)\)
\(=3\left[1+4 \sin ^{2} x \cos ^{2} x-4 \sin x \cos x\right]\)
\(\quad+6+12 \sin x \cos x+4\left[\left(\sin ^{2} x+\cos ^{2} x\right)^{2}\right.\)
\(\left.\quad-2 \sin ^{2} x \cos ^{2} x-\sin ^{2} x \cos ^{2} x\right]\)
\(+4\left(\sin ^{6} x+\cos ^{6} x\right)\)
\(=3(1-2 \sin x \cos x)^{2}+6(1+2 \sin x \cos x)\)
\(\quad+4\left(\sin ^{2} x+\cos ^{2} x\right)\left(\sin ^{4} x+\cos ^{4} x\right.\)
\(\left.\quad-\sin ^{2} x \cos ^{2} x\right)\)
\(=3\left[1+4 \sin ^{2} x \cos ^{2} x-4 \sin x \cos x\right]\)
\(\quad+6+12 \sin x \cos x+4\left[\left(\sin ^{2} x+\cos ^{2} x\right)^{2}\right.\)
\(\left.\quad-2 \sin ^{2} x \cos ^{2} x-\sin ^{2} x \cos ^{2} x\right]\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \( 2\left[\begin{array}{ll}1 & 3 \\ 0 & x\end{array}\right]+\left[\begin{array}{ll}y & 0 \\ 1 & 2\end{array}\right]=\left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right] \) then the value of \( x \) and \( y \) areKCET 2017 Easy
- The general solution of \(|\sin x|=\cos x\) is (when \(\mathrm{n} \in \mathrm{I}\) ) given byKCET 2008 Easy
- The value of the expression \( \tan \left(\frac{1}{2} \cos ^{-1} \frac{2}{\sqrt{5}}\right) \) isKCET 2018 Hard
- The general solution of \(\left(\frac{d y}{d x}\right)^{2}=1-x^{2}-y^{2}+x^{2} y^{2}\) isKCET 2011 Easy
- The smallest positive divisor greater than 1 of a composite number \(a\) isKCET 2013 Medium
- The area of the parallelogram whose adjacent sides are \( \hat{i}+\hat{k} \) and \( 2 \hat{i}+\hat{j}+\hat{k} \) isKCET 2014 Hard
More PYQs from KCET
- If \((\mathbf{a} \times \mathbf{b})^{2}+(\mathbf{a} \cdot \mathbf{b})^{2}=144\) and \(|\mathbf{a}|=4\), then \(|\mathbf{b}|\) is equal toKCET 2012 Easy
- A true breeding plant producing red flowers is crossed with a pure plant producing white flowers. Allele for red colour of flower is dominant. After selfing the plants of first filial generation, the proportion of plants producing white flowers in the progeny would beKCET 2009 Medium
- EcoRI cleaves the DNA strands to produceKCET 2013 Easy
- Incorrectly matched pair isKCET 2020 Easy
- Match List-I with List-II and select the correct options
Codes:List-I (Functional group) List-II (Functional group reagent) (a) 
(i) Neutral ferric chloride test (b) \(\text{C}_6\text{H}_5\text{NH}_2\) (ii) Azo dye test (c) \(\text{CH}_3\text{CH}_2\text{CHO}\) (iii) Ceric ammonium nitrate test (d) 
(iv) Tollen's reagent test KCET 2026 Medium - The value of \(\int_{0}^{4}|x-1| d x\) isKCET 2011 Easy