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Posted by Unique #Seraj Ali ??? 5 years, 4 months ago
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Gaurav Seth 5 years, 4 months ago
Solution:
Let Ф = π/8
2Ф = π/4
tan 2Ф = 1 = 2 tan Ф / [ 1 - tan² Ф ]
1 - tan² Ф = 2 tan Ф
tan² Ф + 2 tan Ф - 1 = 0
tan Ф = 1/2 [ -2 +- √(4 +4) ] = -1 +- √2
tan π/8 is > 0
Therefore, tan π/8 = √2 - 1
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Complex Numbers Class 11 – A number that can be represented in form p + iq is defined as a complex number. [Where, p and q are real numbers and i=−1−−−√]. For a complex number z = p + iq, p is known as the real part, represented by Re z and q is known as the imaginary part represented by Im z of complex number z.

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Gaurav Seth 5 years, 4 months ago
</header>
Definition:
An equation involving one or more trigonometrical ratio of an unknown angle is called a trigonometrical equation

A trigonometric equation is different from a trigonometrical identities. An identity is satisfied for every value of the unknown angle e.g., cos2 x = 1 − sin2 x is true ∀ x ∈ R, while a trigonometric equation is satisfied for some particular values of the unknown angle.
(1) Roots of trigonometrical equation: The value of unknown angle (a variable quantity) which satisfies the given equation is called the root of an equation, e.g., cos θ = ½, the root is θ = 60° or θ = 300° because the equation is satisfied if we put θ = 60° or θ = 300°.
(2) Solution of trigonometrical equations: A value of the unknown angle which satisfies the trigonometrical equation is called its solution.
Since all trigonometrical ratios are periodic in nature, generally a trigonometrical equation has more than one solution or an infinite number of solutions. There are basically three types of solutions:
- Particular solution: A specific value of unknown angle satisfying the equation.
- Principal solution: Smallest numerical value of the unknown angle satisfying the equation (Numerically smallest particular solution).
- General solution: Complete set of values of the unknown angle satisfying the equation. It contains all particular solutions as well as principal solutions.
Trigonometrical equations with their general solution
| Trigonometrical equation | General solution |
| sin θ = 0 | θ = nπ |
| cos θ = 0 | θ = nπ + π/2 |
| tan θ = 0 | θ = nπ |
| sin θ = 1 | θ = 2nπ + π/2 |
| cos θ = 1 | θ = 2nπ |
| sin θ = sin α | θ = nπ + (−1)nα |
| cos θ = cos α | θ = 2nπ ± α |
| tan θ = tan α | θ = nπ ± α |
| sin2 θ = sin2 α | θ = nπ ± α |
| tan2 θ = tan2 α | θ = nπ ± α |
| cos2 θ = cos2 α | θ = nπ ± α |
| sin θ = sin α cos θ = cos α |
θ = nπ + α |
| sin θ = sin α tan θ = tan α |
θ = nπ + α |
| tan θ = tan α cos θ = cos α |
θ = nπ + α |
General solution of the form a cos θ + b sin θ = c

Posted by Arpit Yadav 5 years, 4 months ago
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Gaurav Seth 5 years, 4 months ago
Given: 

and 
Squaring both sides and adding both the equations, we get





and 

and 
[
lies in first quadrant]


Therefore, Polar form of
is 
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Gargi Aggarwal 5 years, 4 months ago
1Thank You