- #1
johncena
- 131
- 1
Can anyone give any hint to solve this ?
If sinx + sin2x + sin3x = 1,
then , cos6x - 4cos4x + 8cos2x =
(a) 1
(b) 4
(c) 2
(d) 3
If sinx + sin2x + sin3x = 1,
then , cos6x - 4cos4x + 8cos2x =
(a) 1
(b) 4
(c) 2
(d) 3
The general strategy for solving equations involving sin and cos is to use trigonometric identities to simplify the equation and then solve for the variable. Some common identities that may be helpful include the Pythagorean identities (sin^2x + cos^2x = 1) and the double angle identities (sin 2x = 2sinx cosx, cos 2x = cos^2x - sin^2x).
It is important to carefully examine the equation and try to identify any patterns or relationships between the terms. This can help determine which identity will be most useful in simplifying the equation. It may also be helpful to have a list of common identities on hand for reference.
While a calculator can be a useful tool for checking answers, it is important to understand the concepts and strategies behind solving trigonometric equations by hand. Calculator use should not be relied upon as a primary method for solving these types of equations.
Yes, there are a few special cases and restrictions to keep in mind. For example, since sine and cosine are periodic functions, there may be multiple solutions to an equation. It is important to find all possible solutions within the given domain. Additionally, some identities may only be valid for certain values of x, so it is important to check for any restrictions before proceeding with simplifying an equation.
Yes, other trigonometric functions can be used in conjunction with sin and cos to solve equations. However, it is important to remember that these functions have their own identities and properties, so they may not always be compatible with the identities and strategies used for sin and cos. It is best to stick with the functions given in the original equation when possible.