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Find the value of cos45sec30+cosec30.

Answer
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Hint: Put the value of cos45, sec30 and cosec30 in the expression and find out its value.

Complete step-by-step answer:

According to the question, we have to calculate the value of cos45sec30+cosec30 .
We know that cos45=12,sec30=23 and cosec30=2. So, putting all these values in the above expression, we’ll get:
cos45sec30+cosec30=1223+2,cos45sec30+cosec30=122+233,cos45sec30+cosec30=32(2+23)
Therefore the value of cos45sec30+cosec30 is 32(2+23).

Note: Since denominator is an irrational number in the above answer, we can also rationalize it to convert it into another form. In rationalization, we multiply the numerator and denominator by the conjugate of the denominator.
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