Dear Readers,
We are providing you trigonometric identity shortcuts which are usually asked in SSC Exams. Use these below short cuts to solve questions within minimum time.
Type-I
In case of sec2x, cosec2x, cot2x and tan2x, we cannot find the maximum value because they can have infinity as their maximum value. So in question containing these trigonometric identities, you will be asked to find the minimum values only. The typical question forms are listed below:
Example: -1
Find the Minimum value of 9 cos 2x + 2 sec 2x
sol - this equation is a typical example of our type-3 so apply the formula 2√ ab so,
- Minimum Value = 2√ 9 x 2= 2√ 18
Example:-2
Find the Minimum value of 8 tan 2x + 7 cot 2x
sol - this equation is a typical example of our type-3 so apply the formula 2√ ab so,
- Minimum Value = 2√ 8 x 7= 2√ 56
Type -II
Example -1
Find the Maximum and Minimum Value of 3 sin x + 4 cos y
Sol- If you find the question of this kind, apply the above formulae.
- Maximum Value = √ 9 + 16 = √ 25 = 5
- Minimum Value = - √ 9 + 16 = - √ 25 = - 5
Example-2
Find the Maximum and Minimum Value of 3 sin x + 2 cos y
Sol- If you find the question of this kind, apply the above formulae.
- Maximum Value = √ 9 + 4 = √ 13
- Minimum Value = - √ 9 + 4 = - √ 13
Type III
Example -1
Find the maximum and Minimum Value of 3 sin 2x + 4 cos 2x
Sol- Here the 4> 3 so
- Maximum Value = 4
- Minimum Value = 3
Example –2
Find the maximum and Minimum Value of 5 sin 2x + 3 cos 2x
Sol - Here 5>3
- Maximum Value = 5
- Minimum Value = 3
Type-IV
Find the Minimum Value of Sec 2x + cosec 2x
Sol - 1 + tan 2x + cosec 2x --------------------------------------------(Sec 2x = 1 + tan 2x)
= 1+ tan 2x + 1 + cot 2x ------------------------------------------------(cosec 2x = 1 + cot 2x )
=2 + tan 2x + cot 2x---------------------------------------------------apply type-3 formula
=2 + 2 √ 1 x 1 = 2 + 2 =4
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