If cos x + cos y = 1/3 and sin x + sin y = 1/4, Find the Values of cos(x+y), sin(x+y) and tan(x+y)
Given cos x+cos y=1/3 and sin x+sin y=1/4, find cos(x+y), sin(x+y) and tan(x+y) using sum-to-product formulas and the tangent half-angle substitution.
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The Coefficient of x⁷ in the Expansion of (1 − x − x² + x³)⁶ Is
AIEEE PYQ: find the coefficient of x⁷ in (1-x-x²+x³)⁶ by first factoring the base as (1-x)²(1+x), then expanding it as a product of two simpler binomials.
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16 sin 20° sin 40° sin 80° Is Equal To
JEE Main 2022 PYQ: evaluate 16 sin20° sin40° sin80° using the identity sin(60°−θ) sinθ sin(60°+θ) = (sin3θ)/4.
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If x^((log₂x)² − 6log₂x + 1) = 64, Then x Is Equal To
Solve x^((log₂x)²−6log₂x+1)=64 by taking log base 2 of both sides and substituting t=log₂x, reducing it to a factorable cubic in t.
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The Number of Six-Digit Numbers That Can Be Formed Using the Digits 1, 3, 5, 7, 9 Such That Each Digit Is Used at Least Once Is
Find how many six-digit numbers can be formed from the digits 1,3,5,7,9 with each digit used at least once, by choosing which digit repeats and arranging the resulting six symbols.
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|z/(z+i)|=2 Represents a Circle — Find Distance of Centre From D(1,5)
The locus |z/(z+i)|=2 in the complex plane is a circle with centre P. Find the distance of P from the point D(1,5) by converting to Cartesian form.
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If k > 0 and the Product of the Roots of the Equation x² − 3kx + 2e^(2 log k) − 1 = 0 Is 7, Then the Sum of the Roots Is
Find the sum of the roots of x^2-3kx+2e^(2logk)-1=0 given k>0 and the product of the roots is 7, by simplifying e^(2logk) to k^2 and using Vieta’s formulas.
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If the Roots of the Equation (a² + b²)x² − 2b(a + c)x + (b² + c²) = 0 Are Equal, Then a, b, c Are in
Show that a, b, c are in geometric progression given the equation (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 has equal roots, by setting the discriminant to zero.
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If √(a + √b) = 3 + √2, Then Find √(a² − b)
Solve sqrt(a + sqrt(b)) = 3 + sqrt(2) for a and b by squaring and matching rational and irrational parts, then find sqrt(a^2 – b).
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If (x³ − 6x² + 10x − 2)/(x² − 5x + 6) = f(x) + A/(x−2) + B/(x−3), Then f(x) Is
Find f(x) in the partial fraction decomposition of (x³−6x²+10x−2)/(x²−5x+6), by performing polynomial long division to separate the quotient from the proper-fraction remainder.