Question

Evaluate:Cos square 40+cos square 50/sin square 40 +sin square 50+4(cos70 cosec20)/7(tan5 tan25 tan65 tan85)

Answer 1

Answer:

11/7

Step-by-step explanation:

We need to convert the numerator and denominator in the first part to sin and cos respectively

so that we can make the angles same and apply the formulas as per the pic you will find the first part reduce to 1 and second to 4/7

by applying formulas

Please check complete solution in the solution pic attached

Thank you

Answer 2

Answer:

Cos (50) = sin (90-40) = sin (40)

cosec (20)= 1/sin (20) = 1/sin (20) = 1/sin (90-70) = 1 / cos(70)

tan (65) = tan (90-25) =cot (25)

tan (85) = tan (90-5) = cot (5)

[cos$^{2}$ (40)+ cos$^{2}$ (50) /sin$^{2}$ (50)+sin$^{2}$ (40)]

+4 [cos (70) . cosec (20) ] /7 [tan (5) .tan (25) . tan (45). tan (65) . tan(85) =

[cos$^{2}$ (40) + sin$^{2}$ (40) /[sin$^{2}$(50) + cos$^{2}$ (50)]

+4[cos(70) /cos (70)/7 [tan (25) .1cot (25) .cot]

=> 1+4/7

=> 11/7

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@GauravSaxena01