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Question
Evaluate the following: `(3sin37°)/(cos53°) - (5"cosec"39°)/(sec51°) + (4tan23° tan37° tan67° tan53°)/(cos17° cos67° "cosec"73° "cosec"23°)`
Solution
`(3sin37°)/(cos53°) - (5"cosec"39°)/(sec51°) + (4tan23° tan37° tan67° tan53°)/(cos17° cos67° "cosec"73° "cosec"23°)`
= `(3sin(90° - 53°))/(cos53°) - (5"cosec"(90° - 51°))/(sec51°) + (4tan(90° - 67°) tan(90° - 53°) xx 1/(cot67°) xx 1/(cot53°))/(cos(90° - 73°) cos(90° - 23°) xx 1/(sin73°) xx 1/(sin23°)`
= `(3cos53°)/(cos53°) - (5sec51°)/(sec51°) + (4 cos67° cos53° xx 1/(cot67°) xx 1/cot53°)/(sin73° sin23° xx 1/(sin73°) xx 1/sin23°)`
= 3 - 5 + 4
= 2.
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