JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If \(\sin x+\sin ^2 x=1, x \in\left(0, \frac{\pi}{2}\right)\), then \(\left(\cos ^{12} x+\tan ^{12} x\right)+3\left(\cos ^{10} x+\tan ^{10} x+\cos ^8 x+\tan ^8 x\right)+\left(\cos ^6 x+\tan ^6 x\right)\) is equal to :
- A 4
- B 1
- C 3
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \sin x+\sin ^2 x=1 \\ & \Rightarrow \sin x=\cos ^2 x \Rightarrow \tan x=\cos x \end{aligned}\) \(\therefore\) Given expression…
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
- Statement \(-1\) : The equation \(x\, log\, x = 2 - x\) is satisfied by at least one value of \(x\) lying between \(1\) and \(2\) Statement \(-2\) : The function \(f(x) = x\, log\, x\) is an increasing function in \([1, 2]\) and \(g (x) = 2 -x\) is a decreasing function in \([ 1 , 2]\) and the graphs represented by these functions intersect at a point in \([ 1 , 2]\)JEE Mains 2013 Hard
- Let \(\alpha\) and \(\beta\) be real numbers. Consider a \(3 \times 3\) matrix \(A\) such that \(A ^2=3 A +\alpha I\). If \(A ^4=21 A +\beta I\), thenJEE Mains 2023 Hard
- If \(A\) and \(B\) are two events such that \(P(A \cap B)=0.1\), and \(P(A \mid B)\) and \(P(B \mid A)\) are the roots of the equation \(12 x^2-7 x+1=0\), then the value of \(\frac{\mathrm{P}(\overline{\mathrm{A}} \cup \overline{\mathrm{B}})}{\mathrm{P}(\overline{\mathrm{A}} \cap \overline{\mathrm{B}})}\) is :JEE Mains 2025 Hard
- \({ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}\) if and only if :JEE Mains 2024 Hard
- Two poles, \(\mathrm{AB}\) of length \(a\) metres and \(\mathrm{CD}\) of length \(\mathrm{a}+\mathrm{b}(\mathrm{b} \neq \mathrm{a})\) metres are erected at the same horizontal level with bases at \(\mathrm{B}\) and \(\mathrm{D} .\) If \(\mathrm{BD}=\mathrm{x}\) and \(\tan \angle\,ACB=\frac{1}{2}\), then:JEE Mains 2021 Hard
- If the common tangents to the parabola, \(x^2 = 4y\) and the circle, \(x^2 + y^2 = 4\) intersect at the point \(P\), then find the square of the slope of the line:JEE Mains 2017 Hard
More PYQs from JEE Mains
- If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity \(e\) of the ellipse satisfiesJEE Mains 2020 Hard
- The sum of all the real roots of the equation \(\left( e ^{2 x }-4\right)\left(6 e ^{2 x }-5 e ^{ x }+1\right)=0\) isJEE Mains 2022 Hard
- A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform speed. At that point, angle of depression of the boat with the man's eye is \(30^{\circ}\) (Ignore man's height). After sailing for \(20\) seconds, towards the base of the tower (which is at the level of water), the boat has reached a point \(B\), where the angle of depression is \(45^{\circ}\). Then the time taken (in seconds) by the boat from \(B\) to reach the base of the tower isJEE Mains 2021 Hard
- Let \(\vec{a}=6 \hat{i}+\hat{j}-\hat{k}\) and \(\vec{b}=\hat{i}+\hat{j}\). If \(\vec{c}\) is a is vector such that \(|\vec{c}| \geq 6, \vec{a} \cdot \vec{c}=6|\vec{c}|,|\vec{c}-\vec{a}|=2 \sqrt{2}\) and the angle between \(\vec{a} \times \vec{b}\) and \(\vec{c}\) is \(60^{\circ}\), then \(|(\vec{a} \times \vec{b}) \times \vec{c}|\) is equal to :JEE Mains 2024 Hard
- If \(f:R \to R\) is a differentiable function and \(f\left( 2 \right) = 6\), then \(\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f\left( x \right)} {\frac{{2\,tdt}}{{\left( {x - 2} \right)}}} \) isJEE Mains 2019 Hard
- Let a circle \(C\) pass through the points \((4,2)\) and \((0,2)\), and its centre lie on \(3 x+2 y+2=0\). Then the length of the chord, of the circle \(C\), whose mid-point is \((1,2)\), is :JEE Mains 2025 Medium