Question

If cosec A = 2, find the value of $\frac{1}{tan A}+\frac{sin A}{1+cos A}$.

Answer 1

SOLUTION IS IN THE ATTACHMENT.

** Trigonometry is the study of the relationship between the sides and angles of a triangle.

The ratio of the sides of a right angled triangle with respect to its acute angles are called trigonometric ratios.

** For any acute angle in a right angle triangle the side opposite to the acute angle is called a perpendicular(P),  the side adjacent to this acute angle is called the base(B) and side opposite to the right angle is called the hypotenuse(H).

** Find the third  side of the right ∆ ABC by using Pythagoras theorem (AC² = AB² + BC²).

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Answer 2

here is your answer OK



cosecA =2

=> sinA = 1/2 ……….(1)

So, cosA = √(1-sin²A)

=> √(1 - 1/4)

=>√(3/4)

=> √3/2 ………….(2)

So, tanA = 1/2 / √3/2

= (1/2) * (2/√3)

= 1/√3 …………(3)

Now in 1/tanA + sinA/(1+cosA)

By (1), (2) & (3), put the values…

= 1/(1/√3) + (1/2) / ( 1+ √3/2)

= √3 + (1/2) / {(2+√3)/2}

= √3 + 1/(2+√3)

= (2√3 + 3 + 1) / (2+√3)

= 2( √3+2) / (√3+2)


OK I hope I help you
= 2