(i) `sec(cos^(-1)""(1)/(2))` का मान ज्ञात कीजिए।
(ii) समीकरणों `sin^(-1)x+sin^(-1)y=(2pi)/(3)` और `cos^(-1)x-cos^(-1)y=(pi)/(3)` को हल कीजिए।
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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 values of the following (i) `sin^(-1) (sin 1)` (ii) `sin^(-1) (sin 2)` (iii) `sin^(-1) (sin 10)` (iv) `sin^(-1) (sin 20)` (v) `sin^
(i) Since `1 in [-pi//2, pi//2], sin^(-1) (sin 1) = 1` (ii) Since `2 in [-pi//2, pi//2], sin^(-1) (sin 2) != 2` `:. Sin^(-1) (sin 2) = sin^(-1) (sin (pi)...
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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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Find the following values : (a) `tan^(1) tan.(13pi)/(5)` (b) `sec^(-1) sec.(13pi)/(3)` (c) `sin^(-1) sin.(33pi)/(5)` (d) `sin^(-1) (sin 8)` (e) `tan^(
Correct Answer - (a) `-(2pi)/(5)` (b) `(pi)/(3)` (c) `(2pi)/(5)` (d) `3 pi -8` (e) `10 - 3 pi` (f) `9 - 2pi` (g) `6 - pi` (h) `7 - 2pi` (a)...
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For `0<theta<2pi,sin^(-1)(sintheta)>cos^(-1)(sintheta)i st r u ew h e n` `(pi/4,pi)` (b) `(pi,(3pi)/2)` `(pi/4,(3pi)/4)` (d) `((3pi)/4,2pi)`
Correct Answer - C `sin^(-1) (sin theta) gt (pi)/(2) - sin^(-1) (sin theta)` `rArr sin^(-1) (sin theta) gt (pi)/(4)` `rArr sin theta gt (1)/(sqrt2)` `rArr (pi)/(4) lt theta lt (3pi)/(4)`
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For `x, y, z, t in R, sin^(-1) x + cos^(-1) y + sec^(-1) z ge t^(2) - sqrt(2pi t) + 3pi` The principal value of `cos^(-1) (cos 5t^(2))` is
Correct Answer - B `sin^(-1) x in [-(pi)/(2), (pi)/(2)]` `cos^(-1) y in [0, pi]` `sec^(-1) z in [0, (pi)/(2)) uu ((pi)/(2), pi]` `rArr sin^(-1) x + cos^(-1) y + sec^(-1) z...
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For `x, y, z, t in R, sin^(-1) x + cos^(-1) y + sec^(-1) z ge t^(2) - sqrt(2pi t) + 3pi` The value of `cos^(-1) ("min" {x, y, z})` is
Correct Answer - C `sin^(-1) x in [-(pi)/(2), (pi)/(2)]` `cos^(-1) y in [0, pi]` `sec^(-1) z in [0, (pi)/(2)) uu ((pi)/(2), pi]` `rArr sin^(-1) x + cos^(-1) y + sec^(-1) z...
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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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`d/(dx)sqrt((1-sin2x)/(1+sin2x))i se q u a lto,(0<x<pi/2),` `sec^2x` (b) `-sec^2(pi/4-x)` `sec^2(pi/4+x)` (d) `sec^2(pi/4-x)`
`y=sqrt((1-sin 2x)/(1+ sin 2x))=(cos x - sin x)/(cos x + sin x)=(1-tan x)/(1+ tan x)=tan ((pi)/(4)-x)` `therefore (dy)/(dx)=-sec^(2)((pi)/(4)-x)`
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Find the values of the following :- `{:((a)sin390^(@)"",(b)cos 405^(@)),((c)tan420^(@)"",(d)cos 450^(@)),((e)sin(2pi+(pi)/(6)),(f)cos(2pi+(pi)/(3))):}
Correct Answer - `{:((a)(1)/(2),(b)(1)/(sqrt(2)),(c)sqrt(3)),((d)0,(e)(1)/(2),(f)(1)/(2)):}`
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