Evaluate cos²30⁰ + sin²45⁰- \(\frac {1}{3}\) tan² 60⁰.

3

(a)

Find the value of \(\frac { \cos { { 60 }^{ 0 } } +\sin { { 45 }^{ 0 } } -\cot { { 30 }^{ 0 } } }{ \tan { { 60 }^{ 0 } } +\sec { { 45 }^{ 0 } } -cosec{ 30 }^{ 0 } } .\)

3

(a)

If \(2\cos { 3\theta } =\sqrt { 3 } \),  find the value of \(\theta\) .

3

(a)

If sin (A – B) = \(\frac{1}{2}\) cos (A + B) = \(\frac{1}{2}\) 0° < A + B \(\leq\) 90°, A > B, find A and B.

3

(a)

If tan (3x + 30⁰) = 1, find the value of x.

3

(a)

Find acute angles A and B, if sin (A + 2B)=\(\frac { \sqrt { 3 } }{ 2 } \) and cos (A + 4B) = 0⁰ , A > B.

3

(a)

Evaluate \(\frac { \tan { { 50 }^{ 0 } } +\sec { { 50 }^{ 0 } } }{ \cot { { 40 }^{ 0 } } +cosec{ 40 }^{ 0 } } +\cos { { 40 }^{ 0 } } cosec{ 50 }^{ 0 }\)

3

(a)

If sin 3A = cos (A - 26°), where 3A is an acute angle, find the value of A.

3

(a)

If sec 5 A = cosec (A + 30⁰), find A. where 5 A is an acute angle, then find the value of A.

3

(a)

Evaluate \(\frac { \sin { { 70 }^{ 0 } } }{ \cos { { 20 }^{ 0 } } } +\frac { cosec{ 36 }^{ 0 } }{ \sec { { 54 }^{ 0 } } } -\frac { 2\cos { { 43 }^{ 0 } } cosec{ 47 }^{ 0 } }{ \tan { { 10 }^{ 0 } } \tan { { 40 }^{ 0 } } \tan { { 50 }^{ 0 } } \tan { { 80 }^{ 0 } } } \)

3

(a)

Evaluate \(\frac { \sec ^{ 2 }{ (\sin { { 90 }^{ 0 } } -\theta ) } -\cot ^{ 2 }{ \theta } }{ 2(\sin ^{ 2 }{ { 25 }^{ 0 } } +\sin ^{ 2 }{ { 65 }^{ 0 } } ) } +\frac { 2\cos ^{ 2 }{ { 60 }^{ 0 } } \tan ^{ 2 }{ { 28 }^{ 0 } } \tan ^{ 2 }{ { 62 }^{ 0 } } }{ \sin ^{ 2 }{ { 30 }^{ 0 } } \cos ^{ 2 }{ { 60 }^{ 0 } } } \)

3

(a)

Prove that \(\cos { \theta } \sin { \theta } -\frac { \sin { \theta } \cos { ({ 90 }^{ 0 }-\theta ) } \cos { \theta } }{ cosec({ 90 }^{ 0 }-\theta ) } -\frac { \cos { \theta } \sin { ({ 90 }^{ 0 }-\theta ) } \sin { \theta } }{ \sec { ({ 90 }^{ 0 }-\theta ) } } +cosec({ 90 }^{ 0 }-\theta )=\frac { 1 }{ \cos { \theta } } .\)

3

(a)

Prove that \(\frac { cosec\theta +cot\theta }{ cosec\theta -cot\theta } =1+2{ cot }^{ 2 }\theta +2{ cosec }^{ 2 }\theta cos\theta \)

3

(a)

Without using trigonometric tables, evaluate \(\frac { \sec { { 39 }^{ 0 } } }{ cosec{ 51 }^{ 0 } } +\frac { 2 }{ \sqrt { 3 } } \tan { { 17 }^{ 0 } } \tan { { 38 }^{ 0 } } \tan { { 60 }^{ 0 } } \tan { { 52 }^{ 0 } } \tan { { 73 }^{ 0 } } -3(\sin ^{ 2 }{ { 31 }^{ 0 } } +\sin ^{ 2 }{ { 59 }^{ 0 } } ).\)

3

(a)

Simplify \(\frac { \tan { { 28 }^{ 0 } } }{ \cot { { 62 }^{ 0 } } } \div \frac { 1 }{ \sqrt { 3 } } [\tan { { 20 }^{ 0 } } .\tan { { 60 }^{ 0 } } .\tan { { 70 }^{ 0 } } ]\)

3

(a)