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IF tan(pie cosa)=cot(pie sina) prove that: cos(a-45)=1/2√2

IF  tan(pie cosa)=cot(pie sina)


prove that: cos(a-45)=1/2√2

Grade:11

3 Answers

Rahul askIITiansExpert.IITR
110 Points
10 years ago
the problem is fairly simple

cot x = tan ( pie/2 - x ).

so, pie/2-piesina = piecosa

1/2-sina=cosa

cosa+sina=1/2

cosa/√2 +sina/√2 =1/2√2

cos(a-45)=1/2√2

hence

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Rahul- IIT Roorkee
yash mittal
31 Points
10 years ago

tan(piecosa) = cot(piesina)

yash mittal
31 Points
10 years ago

tan(piecosa) = cot(piesina)                                                                                                                                              tan(piecosa) = tan(90-180sina)                                                                                                                                       cosa + sina= 90                                                                                                                                                             cos(45-a) =1by2root2  (multiplying and div both sides by 1by root2)                                                                                                                                                                                     hence proved

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