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Determine whether an Equation is Identity or not
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Determine Whether an Equation is Identity or not
STEP I: Replace the variable in the given equation by 0, 30, 45, 60, and 90 one by one.
STEP II: If the LHS of the given equation is not equal to its RHS for some values of mentioned in step I, then it is not an identity.
If all values of the variable mentioned in Step I satisfy the given equation, then simplify the LHS and RHS of the given equation to see whether the two sides are equal or not. If two sides are equal, the equation is an identity.
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Example: Determine whether the equation is an identity or not:
cot2 + cos= sin2
Solution: We have cot2 + cos= sin2
Here, cot is not defined for = 0. So, can take the values satisfying  0 < 90.
When = 90, you have
LHS = cot2 90 + cos 90 = 0 and RHS = sin 90 = 1
Clearly, LHS RHS, when = 90
Thus, the given equation is not an identity.
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