Evaluate 11sin70/7cos20-4/7 (cos53cosec37 /tan35tan55tantan45)
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11sin70°/7cos20° - 4/7( cos53° cosec37° )/(tan35° tan55° tan45°)
we know,
sin(90-Ф) cosФ
∴ sin70° = sin(90-20) = cos20°
Similarly cos(90 - Ф) = sinФ
∴ cos53° = cos(90 - 37) = sin37°
And tan(90-Ф) = cotФ
∴tan35 = tan(90-55) = cot55
Now, 11cos20/7cos20 - 4/7(sin37.cosec37)/(cot55.tan55.tan45)
= 11/7 - 4/7
= (11 - 4)/7 = 1
Hence, answer is 1
we know,
sin(90-Ф) cosФ
∴ sin70° = sin(90-20) = cos20°
Similarly cos(90 - Ф) = sinФ
∴ cos53° = cos(90 - 37) = sin37°
And tan(90-Ф) = cotФ
∴tan35 = tan(90-55) = cot55
Now, 11cos20/7cos20 - 4/7(sin37.cosec37)/(cot55.tan55.tan45)
= 11/7 - 4/7
= (11 - 4)/7 = 1
Hence, answer is 1
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