## extending trigonometry

1. given that cot @ = surd 2, find the value of 1/ ( cos square @ - 2sin@cos@)

2. given that sin @ cot @ = 60/169, pai/4 <= @ < = pai/2, find the value of tan @

3. given that tan @ + cot @ =9/12, find the value of tan square @ + sec @ cosec @ + cot square @

4. given that tan @ = 2, find values of :

i. (4sin@ -2 cos@) / ( 5sin @ + 3sin @)

ii. 2/3 (sin square @) + 1/4 ( cos square @)

iii. sin @ cos cube @

5. simplify the followings:

i. surd (1-2sin10degreecos10degree) / (cos 10 degree - surd (1-sin square 100))

ii. tan (90 degree - @ ) - ((cot squarre @ sin square (90 degree - @)) / (cot @+cos @))

6. find the values of the following

tan (pai/5) + tan (2pai/5) + tan (3pai/5) + tan (4pai/5)

7. prove the following identities

i. (sec @ -cosec @) / (tan @ - cot @) = (tan @ + cot @)/ (sec @ + cosec @)

ii. ( 1-sin@ + cos @) / (1-sin @) = ( 1 + sin @ + cos @ ) / cos @

p/s: please help me answer these questions...sorry i need to spell some pf math's symbol because i don't know how to write it in symbol... help me as soon as possible...thanks!!!