Without using tables, evaluate the following:csc257o−tan233osec254o−cot236o+2sin238o.sec252o−sin245o.

We have, csc257o−tan233osec254o−cot236o+2sin238o.sec252o−sin245o.=csc2(90o−33o)−tan233osec2(90o−36o)−cot236o+2sin238o.sec2(90o−38o)−sin245o=sec233o−tan233ocsc236o−cot236o+2sin238o.csc238o−(21)2=11+2.1−21=3−21=25.

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Without using tables, evaluate the following: {^2 54^o -^2 36^

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Without using tables, evaluate the following:
$\frac{sec ^{2} 5 4 ^{o} - cot ^{2} 3 6 ^{o}}{csc ^{2} 5 7 ^{o} - tan ^{2} 3 3 ^{o}} + 2 sin^{2} 3 8^{o} . sec^{2} 5 2^{o} - sin^{2} 4 5^{o}$ .

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Without using tables, evaluate the following:

\frac{sec ^{2} 5 4 ^{o} - cot ^{2} 3 6 ^{o}}{csc ^{2} 5 7 ^{o} - tan ^{2} 3 3 ^{o}} + 2 sin^{2} 3 8^{o} . sec^{2} 5 2^{o} - sin^{2} 4 5^{o}

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Text solutionVerified

We have,

\frac{sec ^{2} 5 4 ^{o} - cot ^{2} 3 6 ^{o}}{csc ^{2} 5 7 ^{o} - tan ^{2} 3 3 ^{o}} + 2 sin^{2} 3 8^{o} . sec^{2} 5 2^{o} - sin^{2} 4 5^{o}

= \frac{sec ^{2} ( 9 0 ^{o} - 3 6 ^{o} ) - cot ^{2} 3 6 ^{o}}{csc ^{2} ( 9 0 ^{o} - 3 3 ^{o} ) - tan ^{2} 3 3 ^{o}} + 2 sin^{2} 3 8^{o} . sec^{2} (9 0^{o} - 3 8^{o}) - sin^{2} 4 5^{o}

= \frac{csc ^{2} 3 6 ^{o} - cot ^{2} 3 6 ^{o}}{sec ^{2} 3 3 ^{o} - tan ^{2} 3 3 ^{o}} + 2 sin^{2} 3 8^{o} . csc^{2} 3 8^{o} - (\frac{1}{2})^{2}

= \frac{1}{1} + 2.1 - \frac{1}{2} = 3 - \frac{1}{2} = \frac{5}{2}

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Question Text	Without using tables, evaluate the following: $\frac{sec ^{2} 5 4 ^{o} - cot ^{2} 3 6 ^{o}}{csc ^{2} 5 7 ^{o} - tan ^{2} 3 3 ^{o}} + 2 sin^{2} 3 8^{o} . sec^{2} 5 2^{o} - sin^{2} 4 5^{o}$ .
Answer Type	Text solution:1
Upvotes	150

Without using tables, evaluate the following:csc257o−tan233osec254o−cot236o​+2sin238o.sec252o−sin245o.

Text solutionVerified

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Without using tables, evaluate the following:
$\frac{sec ^{2} 5 4 ^{o} - cot ^{2} 3 6 ^{o}}{csc ^{2} 5 7 ^{o} - tan ^{2} 3 3 ^{o}} + 2 sin^{2} 3 8^{o} . sec^{2} 5 2^{o} - sin^{2} 4 5^{o}$ .