step 1 The question says that we have to find the value for angle x. Here, the equation is 10 .2x into

Cos^2 x+sinx+1=0 | Numerade

Name: Problem 60, Chapter 12: Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry
Uploaded: 2021-07-31T03:20:39-08:00
Duration: 1 min 13 s
Channel: Tanishq Gupta
Description: cos^2 x+sinx+1=0

Key Concepts

Pythagorean Identity

The Pythagorean identity, which states that sin²? + cos²? = 1, is a fundamental relationship in trigonometry. It allows one to express cosine squared in terms of sine squared (or vice versa), which is particularly useful when solving equations that involve both sine and cosine functions.

Quadratic Equations in Trigonometric Functions

In many trigonometric equations, substitution using identities can lead to a quadratic equation in one trigonometric function. Recognizing and solving such quadratic forms is essential, as it enables the determination of possible values of the trigonometric function by methods such as factoring or the quadratic formula.

Range of Trigonometric Functions

When solving equations involving sine or cosine, it is crucial to consider the range of these functions; for instance, sine and cosine can only take values between -1 and 1. This concept helps in discarding extraneous solutions that may arise algebraically but do not fit within the possible output values of the trigonometric functions.

General Solution of Trigonometric Equations

After finding the valid trigonometric function values, it is important to determine the complete set of angles that satisfy the equation. This involves understanding the periodicity of trigonometric functions and formulating the general solution, which represents all possible solutions in terms of an integer parameter.

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