Prove that sin(n+1) x sin(n+2) x + cos(n+1) x. cos(n+2) x = cosx

2

(a)

In any triangle, if angle are in the ratio 1:2:3, then find their corresponding sides.

2

(a)

A railroad curve is to be laid out on a circle. What radius should be used , if the track is to change direction by \(30^{0}\) is a distance of 50m

2

(a)

If \(cos\theta +sin\theta =\sqrt { 2 } cos\theta \)then prove that \(cos\theta -sin\theta =\sqrt { 2 } sin\theta \).

2

(a)

Prove that cos 55⁰+cos65⁰+cos75⁰=2cos40⁰cos35⁰

2

(a)

Prove that
\(\sqrt { \cfrac { 1-sin\theta }{ 1+sin\theta } } =sec\theta -tan\theta ,if-\cfrac { \pi }{ 2 } <\theta <\cfrac { \pi }{ 2 } -sec\theta +tan\theta ,if\frac { \pi }{ 2 } <\theta <\cfrac { 3\pi }{ 2 } \)

2

(a)

\(If\quad sin\quad A=\cfrac { 3 }{ 5 } ,0

2

(a)

Find the radian measures corresponding to the following degree measures:-47^o30'

2

(a)

Find the radian measures corresponding to the following degree measures240^o

2

(a)

Find the degree measures corresponding to the following radian measures (use \(\pi\) = 22/7)-2^c

2

(a)

Find the degree measures corresponding to the following radian measures (use \(\pi\) = 22/7)\(-({5\pi\over 4})^C\)

2

(a)

Prove that: \(sin^2{\pi\over6}+cos^2{\pi\over3}-tan^2{\pi\over 4}=-{1\over2}\)

2

(a)

Find the general solutions of the following equations tan 2\(\theta =\sqrt{3}\) 

2

(a)

Find the general solutions of the following equations tan 3\(\theta\) = - 1

2

(a)

Find the general solutions of the following equations \(tan \ x={-1\over \sqrt{3}}\)

2

(a)