Trigonometry (Basic)

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #121

If `sin 2\alpha = cos \alpha`, then the value of `tan \alpha` is .......
Ans: `1/\sqrt{3}`
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Question No: #122

If `sin 3\theta = cos (2\theta + 45^\circ)`, then the value of `tan 5\theta` is -
(a) `\sqrt{3}`, (b) `1`, (c) `\frac{1}{\sqrt{3}}`, (d) undefined
Ans: (b) `1`
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Question No: #123

If `sin (2x+y) = cos (4x-y)`, then find the value of `tan 3x`.
Ans: `1`
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Question No: #124

If `sin (5x-18^\circ) = cos (5y+28^\circ)`, then find the value of `x+y`.
Ans: `16^\circ`
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Question No: #125

Prove that, `tan 7^\circ tan 23^\circ tan 60^\circ tan 67^\circ tan 83^\circ = \sqrt{3}`.

Question No: #126

Prove that, `tan 15^\circ + tan 75^\circ = \frac{sec^2 15^\circ}{\sqrt{sec^2 15^\circ - 1}}`

Question No: #127

Prove that, `\frac{sin 52^\circ + cos 38^\circ}{sin 38^\circ + cos 52^\circ} = tan 52^\circ`.

Question No: #128

show that, `\text{cosec}^2 22^\circ cot^2 68^\circ = sin^2 22^\circ + sin^2 68^\circ + cot^2 68^\circ`.

Question No: #129

Show that, `\frac{tan 57^\circ + cot 37^\circ}{tan 33^\circ + cot 53^\circ} = tan 57^\circ cot 37^\circ`.

Question No: #130

Prove that, `\frac{tan 47^\circ + cot 27^\circ}{tan 43^\circ + cot 63^\circ} = cot 43^\circ cot 27^\circ`.