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Published on: 09/10/2019
Trigonometry
Download Tamil Nadu 10th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
The shadow of a tower, when the angle of elevation of the sum is 45o is found to be 10 metres, longer than when it is 60o. find the height of the tower
2.
The angle of elevation of a tower at a point is 45o, After going 20 meters towards the foot of the tower the angle of elevation of the tower becomes 60o calculate the height of the tower.
3.
If tanθ+sinθ=P; tanθ-sinθ=q P.T P2-q2=4\(\sqrt{pq}\)
4.
\(P.T\left( \frac { 1+{ tan }^{ 2 }A }{ 1+{ cot }^{ 2 }A } \right) ={ \left( \frac { 1-tan\quad A }{ 1-cot\quad A } \right) }^{ 2 }={ tan }^{ 2 }A\)
5.
If 15tan2 θ+4 sec2 θ=23 then find the value of (secθ+cosecθ)2 -sin2 θ
6.
P.T (1+tan∝tan∝tanβ)2 +(tan∝-tanβ)2 =sec2 ∝sec2β.
7.
If ATB=90o then prove that
\(\sqrt { \frac { tanA\quad tanB+tanA\quad cotB }{ sinA\quad secB } } -\frac { { Sin }^{ 2 }A }{ { Cos }^{ 2 }A } =tanA\)
8.
If sin 3A = cos (A - 26°), where 3A is an acute angle, find the value at A.
9.
Express the ratios cos A, tan A and sec A in terms of sin A.
10.
If sin (A - B) = \(\frac12\), cos (A + B) = \(\frac12\), 0o < A + ≤ 90°, A > B, find A and B.
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8.
We are given that sin 3A = cos (A - 26°) ...(1)
Since sin 3A = cos(90° - 3A) we can write (1) as
cos (90° - 3A) = cos (A - 26°)
Since 90° - 3A and A - 26° are both acute angles
90° - 3A = A - 26°
which gives A = 29°
9.
Since
cos2A + sin2A = 1 therefore
cos2A = 1 - sin2A
i.e., cos A = 土 \(\sqrt { 1-{ sin }^{ 2 }A } \)
This gives cos A = \(\sqrt { 1-{ sin }^{ 2 }A } \)
Hence, \(tanA=\frac { sinA }{ cosA } =\frac { sinA }{ \sqrt { { 1-sin }^{ 2 }A } } \)
and \(secA=\frac { 1 }{ cosA } =\frac { 1 }{ \sqrt { 1-{ sin }^{ 2 }A } } \)
10.
Since, sin(A - B) = \(\frac12\), ∴ A-B = 30° ..... (1)
Also, since cos (A + B) = \(\frac12\)
∴ A + B = 60° ...(2)
Solving (1) and (2)
A - B + A + B = 30o + 60o
2A = 90o
A = 45o
We get,
A = 45° and B = 15°
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Tamilnadu Stateboard 10th Standard Subjects
Tamilnadu Stateboard Standards
