Question

sin 28°54'÷sec 61°6'+cos 28°54'÷cosec 61°6'​

Answer 1

$\underline{\textsf{To find:}}$

$\textsf{The value of}$

$\mathsf{\dfrac{sin\,28^{\circ}54'}{sec\,61^{\circ}6'}+\dfrac{cos\,28^{\circ}54'}{cosec\,61^{\circ}6'}}$

$\underline{\textsf{Solution:}}$

$\textsf{Formula used:}$

$\boxed{\mathsf{sec\theta=cosec(90^{\circ}-\theta)}}$

$\boxed{\mathsf{cosec\theta=sec(90^{\circ}-\theta)}}$

$\boxed{\mathsf{sin^2A+cos^2A=1}}$

$\textsf{Consider,}$

$\mathsf{\dfrac{sin\,28^{\circ}54'}{sec\,61^{\circ}6'}+\dfrac{cos\,28^{\circ}54'}{cosec\,61^{\circ}6'}}$

$\mathsf{=\dfrac{sin\,28^{\circ}54'}{cosec\,28^{\circ}54'}+\dfrac{cos\,28^{\circ}54'}{sec\,28^{\circ}54'}}$

$\mathsf{=\dfrac{sin\,28^{\circ}54'}{\dfrac{1}{sin\,28^{\circ}54'}}+\dfrac{cos\,28^{\circ}54'}{\dfrac{1}{cos\,28^{\circ}54'}}}$

$\mathsf{=sin^228^{\circ}54'+cos^228^{\circ}54'}$

$\textsf{=1}$

$\implies\boxed{\mathsf{\dfrac{sin\,28^{\circ}54'}{sec\,61^{\circ}6'}+\dfrac{cos\,28^{\circ}54'}{cosec\,61^{\circ}6'}=1}}$

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Answer 2

sin 28°54'÷sec 61°6'+cos 28°54'÷cosec 61°6'