1/tan θ + cot θ =
A. cos θ sin θ
B. sec θ sin θ
C. tan θ cot θ
D. sec θ cosec θ
1 Answers
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cos θ/1−tan θ + sin θ/1−cot θ = ……… A) cos θ – sin θ B) tan θ – cot θ C) cos θ – sin θ D) tan θ + cot θ
Correct option is: C) cos \(\theta\) + sin \(\theta\) \(\frac{cos\theta}{1-tan\theta} + \frac{sin\theta}{1-cot\theta}\)= \(\frac {cos\theta}{\frac {1-sin\theta}{cos\theta}} + \frac {sin\theta}{\frac {1-cos\theta}{sin\theta}}\) = \(\frac {cos^2\theta}{cos\theta - sin \theta} + \frac {sin^2\theta}{sin\theta - cos\theta}\) = \(\frac {cos^2\theta}{cos\theta - sin \theta} - \frac {sin^2\theta}{sin\theta...
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cos θ/1−tan θ + sin θ/1−cot θ = ……… A) cos θ – sin θ B) tan θ – cot θ C) cos θ – sin θ D) tan θ + cot θ
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The value of tan^2θ + tan^4θ A) sec^4θ – sec^2θ B) sec^2θ – sec^4θ C) sin^2θ – cos^2θ D) sec^2θ – tan^2θ
Correct option is: A)\(sec^4\theta - sec^2\theta\) \(tan^2 \theta + tan^4 \theta\) = \(tan^2\theta (1+ tan^2\theta) \) = \(tan^2\theta.sec^2\theta \) (\(\because\) 1 + \(tan^2\theta= sec^2 \theta\)) = \((sec^2\theta-1) sec ^2\theta \) (\(\because\) \(tan^2\theta= sec^2 \theta\)-1) = \(sec^4\theta - sec^2\theta\)
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The value of tan^2θ + tan^4θ A) sec^4θ – sec^2θ B) sec^2θ – sec^4θ C) sin^2θ – cos^2θ D) sec^2θ – tan^2θ
2 Answers
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Sin^3 θ Cos θ + Cos^3 θ Sin θ = A) Sin θ + Cos θ B) Sin θ Cos θ C) Sin θ D) Cot θ
Correct option is: B) Sin θ Cos θ \(Sin^3 \theta \, Cos \theta + Cos^3 \theta \, Sin \theta =\) sin \(\theta\) cos \(\theta\) (\(sin^2\theta + cos^2\theta\)) = sin \(\theta\) .cos \(\theta\) (\(sin^2\theta + cos^2\theta\) = 1)
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If `theta-phi=pi/2,` prove that, `[(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,
Correct Answer - C `AB=[(cos^(2) theta,),(cos theta sin theta,)][(cos^(2) phi,cos phi sin phi),(cos phi sin phi,sin^(2) phi)]` `=[(cos^(2) theta cos^(2) phi+cos theta cos phi sin theta sin phi ,cos^(2)theta cos phi...
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Find the principal value of the following (i) `cos^(-1) (cos 3)` (ii) `cos^(-1) (cos 4)` (iii) `cos^(-1) (cos 15)` (iv) `cos^(-1) (cos 30)` (v) `cos^(
(i) Since `3 in [0, pi], cos^(-1) (cos 3) = 3` (ii) Since `4 !in [0, pi], cos^(-1) (cos 4) != 4` `:. Cos^(-1) (cos 4) = 2pi - 4`...
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If `cosec^(-1) (cosec x) and cosec (cosec^(-1) x)` are equal function then the maximum range of value of x is
Correct Answer - A `cosec (cosec^(-1) x) = x AA x in R -(-1, 1)` Also range of `cosec^(-1) (cosec x) in [-(pi)/(2), 0) uu (0, (pi)/(2]` So combing these two,...
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सरल कीजिए, ` cos theta [{:( cos theta,, sin theta ), (-sin theta,, cos theta ):}] + sin theta [ {:(sin theta ,, - cos theta ), (cos theta ,, sin theta
Correct Answer - `[{:(,1,0),(,1,1):}]`
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