
If , then can be reduced to?
Answer
479.7k+ views
Hint: Here, we will write the RHS of the given equation in terms of cos function by using the trigonometric value. , find the value of . Substituting the value of in and solving it further using the trigonometric identities, we will get the required reduced value of .
Formula Used:
We will use the formula
Complete step-by-step answer:
It is given that .
Now, we know that the value of
Hence, substituting the value of 0 in the RHS of , we get
Cancelling cos function from both sides, we get
Subtracting from both sides, we get
………………………….
Now, we have to reduce the value of .
Now, substituting the value of from equation into , we get
Now, using the formula , we get
Hence, if , then can be reduced to .
Therefore, this is the required answer.
Note: Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Identity inequalities are true for every value occurring on both sides of an equation. Geometrically, these identities involve certain functions of one or more angles. There are various distinct identities involving the side length as well as the angle of a triangle. The trigonometric identities hold true only for the right-angle triangle. The six basic trigonometric ratios are sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. All the fundamental trigonometric identities are derived from the six trigonometric ratios.
Formula Used:
We will use the formula
Complete step-by-step answer:
It is given that
Now, we know that the value of
Hence, substituting the value of 0 in the RHS of
Cancelling cos function from both sides, we get
Subtracting
Now, we have to reduce the value of
Now, substituting the value of
Now, using the formula
Hence, if
Therefore, this is the required answer.
Note: Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Identity inequalities are true for every value occurring on both sides of an equation. Geometrically, these identities involve certain functions of one or more angles. There are various distinct identities involving the side length as well as the angle of a triangle. The trigonometric identities hold true only for the right-angle triangle. The six basic trigonometric ratios are sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. All the fundamental trigonometric identities are derived from the six trigonometric ratios.
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