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In ∆ABC, prove that `(cos 2"A")/"a"^2 - (cos 2"c")/"c"^2 = 1/"a"^2 - 1/"c"^2`
Concept: Solutions of Triangle>Polar Co-Ordinates
In ∆ABC, if `(2cos "A")/"a" + (cos "B")/"b" + (2cos"C")/"c" = "a"/"bc" + "b"/"ca"`, then show that the triangle is a right angled
Concept: Solutions of Triangle>Polar Co-Ordinates
In ∆ABC, prove that `sin ((A - B)/2) = ((a - b)/c) cos C/2`
Concept: Solutions of Triangle>Polar Co-Ordinates
In ΔABC, prove that `("a"^2sin("B" - "C"))/(sin"A") + ("b"^2sin("C" - "A"))/(sin"B") + ("c"^2sin("A" - "B"))/(sin"C")` = 0
Concept: Solutions of Triangle>Polar Co-Ordinates
In ΔABC, prove that `("b"^2 - "c"^2)/"a" cos"A" + ("c"^2 - "a"^2)/"b" cos"B" + ("a"^2 - "b"^2)/"c" cos "C"` = 0
Concept: Solutions of Triangle>Polar Co-Ordinates
Find the principal solutions of cot θ = 0
Concept: Trigonometric Equations and Their Solutions
Find the cartesian co-ordinates of the point whose polar co-ordinates are `(1/2, π/3)`.
Concept: Solutions of Triangle>Polar Co-Ordinates
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
Concept: Trigonometric Equations and Their Solutions
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
Concept: Trigonometric Equations and Their Solutions
Find p and q if the equation px2 – 8xy + 3y2 + 14x + 2y + q = 0 represents a pair of prependicular lines.
Concept: General Second Degree Equation
Find the combined equation of the following pair of lines:
2x + y = 0 and 3x − y = 0
Concept: Combined Equation of a Pair Lines
Find the combined equation of the following pair of lines passing through point (2, 3) and parallel to the coordinate axes.
Concept: Combined Equation of a Pair Lines
Find the combined equation of the following pair of line passing through (−1, 2), one is parallel to x + 3y − 1 = 0 and other is perpendicular to 2x − 3y − 1 = 0
Concept: Combined Equation of a Pair Lines
Find the separate equation of the line represented by the following equation:
3y2 + 7xy = 0
Concept: Combined Equation of a Pair Lines
Find k, the slope of one of the lines given by kx2 + 4xy – y2 = 0 exceeds the slope of the other by 8.
Concept: Homogeneous Equation of Degree Two
If one of the lines given by ax2 + 2hxy + by2 = 0 bisects an angle between the coordinate axes, then show that (a + b)2 = 4h2.
Concept: Homogeneous Equation of Degree Two
Find the coordinates of the points of intersection of the lines represented by x2 − y2 − 2x + 1 = 0
Concept: General Second Degree Equation
The area of triangle formed by the lines x2 + 4xy + y2 = 0 and x - y - 4 = 0 is ______.
Concept: Combined Equation of a Pair Lines
Find the joint equation of the line passing through the origin having slopes 2 and 3.
Concept: Combined Equation of a Pair Lines
Show that the difference between the slopes of the lines given by (tan2θ + cos2θ)x2 − 2xy tan θ + (sin2θ)y2 = 0 is two.
Concept: Angle between Lines Represented by ax² + 2hxy + by² = 0
