RS Aggarwal Solutions Class 10 Chapter 8 - Trigonometric Identities (Ex 8A) Exercise 8.1 - Free PDF
FAQs on RS Aggarwal Solutions Class 10 Chapter 8 - Trigonometric Identities (Ex 8A) Exercise 8.1
1. What are Pythagorean Trigonometric Identities according to RS Aggarwal Solutions Class 10 Chapter 8 - Trigonometric Identities (Ex 8A) Exercise 8?
The Pythagorean Trigonometric Identities are derived from Pythagoras' theorem in trigonometry. The Pythagoras theorem is applied to the right-angled triangle below, yielding:
Opposite2 + Adjacent2 = Hypotenuse2
Dividing both sides by Hypotenuse2
Opposite2/Hypotenuse2 + Adjacent2/Hypotenuse2 = Hypotenuse2/Hypotenuse2
sin2θ + cos2θ = 1
One of the Pythagorean identities is this. We can derive two more Pythagorean Trigonometric Identities in the same way.
1 + tan2θ = sec2θ
1 + cot2θ = cosec2θ
Now you might have a clear understanding of what Pythagorean Trigonometric Identities mean and also their kinds.
2. What do you contemplate with complementary and supplementary Trigonometric Identities according to RS Aggarwal Solutions Class 10 Chapter 8 - Trigonometric Identities (Ex 8A) Exercise 8?
Complementary angles are a pair of two angles whose sum equals 90°.
sin (90°- θ) = cos θ
cos (90°- θ) = sin θ
cosec (90°- θ) = sec θ
sec (90°- θ) = cosec θ
tan (90°- θ) = cot θ
cot (90°- θ) = tan θ
The supplementary angles are a pair of two angles whose sum equals 180°.
sin (180°- θ) = sinθ
cos (180°- θ) = -cos θ
cosec (180°- θ) = cosec θ
sec (180°- θ)= -sec θ
tan (180°- θ) = -tan θ
cot (180°- θ) = -cot θ
3. What do you understand by sum and difference Trigonometric Identities?
The formulas sin(X+Y), cos(X-Y), cot(X+Y), and others are part of the sum and difference identities.
sin (X+Y) = sin X cos Y + cos X sin Y
sin (X-Y) = sin X cos Y - cos X sin Y
cos (X+Y) = cos X cos Y - sin X sin Y
cos (X-Y) = cos X cos Y + sin X sin Y
\[\tan \left ( X+Y \right ) = \frac{\left ( \tan X+\tan Y \right )}{1-\tan X \tan Y }\]
\[\tan \left ( X-Y \right ) = \frac{\left ( \tan X-\tan Y \right )}{1+\tan X \tan Y }\]
4. How is a Sine Rule described in RS Aggarwal Solutions Class 10 Chapter 8 - Trigonometric Identities (Ex 8A) Exercise 8?
It is the ratio of the side opposite a given angle (in a right-angled triangle) to the hypotenuse is the trigonometric function. The sine rule describes the relationship between a triangle's angles and their corresponding sides. We'll have to use the sine rule to solve non-right-angled triangles. The sine rule can be written as follows for a triangle with sides 'x', 'y', and 'z' and opposite angles X, Y, and Z.
\[\frac{x}{\sin X}=\frac{y}{\sin Y}=\frac{z}{\sin Z}\]
\[\frac{\sin X}{x}=\frac{\sin Y}{y}=\frac{\sin Z}{z}\]
\[\frac{x}{y}=\frac{\sin X}{\sin Y};\frac{y}{z}=\frac{\sin Y }{\sin Z};\frac{x}{z}=\frac{\sin X}{\sin Z}\]
5. What is a Cosine Rule according to RS Aggarwal Solutions Class 10 Chapter 8 - Trigonometric Identities (Ex 8A) Exercise 8?
It is the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse is the trigonometric function. When two sides and the included angle of a triangle are given, the cosine rule is used to determine the relationship between the angles and the sides. The sine rule can be written as follows for a triangle with sides 'x', 'y', and 'z' and opposite angles X, Y, and Z.
x2 = y2 + z2 - 2yz·cosX
y2 = z2 + x2 - 2zx·cosY
z2 = x2 + y2 - 2xy·cosZ