Question

( cos 9° + sin 9° ) / ( cos 9º – sin 9° ) = ?

Options :-

( A ) sin 54°
( B ) cos 54°
( C ) tan 54°
( D ) cot54°
​​

Answer 1

$\bigstar$ Explanation $\bigstar$

$\leadsto$ Solution:-

We can write 9 in terms of 45 and 54

54 - 45 = 9

Tan on both sides

tan(54 - 45) = tan(9)

We know that $\rm \tan(A-B) = \frac{tanA - tanB}{1 + tanAtanB}$

Therefore,

$\dfrac{\tan54 - \tan45}{1+tan45tan54} = \dfrac{\sin9}{cos9}$

We know that tan 45 = 1

Therefore,

$\rm \dfrac{tan54 - 1}{1+tan54} = \dfrac{sin9}{cos9}$

$\rm \dfrac{1+tan54}{tan54-1} = \dfrac{cos9}{sin9}$

Using componendo - dividendo

$\dfrac{1+tan54+tan54-1}{1+tan54-tan54+1} = \dfrac{cos9+sin9}{cos9-sin9}\\\\ \dfrac{2tan54}{2} = \dfrac{cos9+sin9}{cos9-sin9}$

Therefore,

$\dfrac{cos9+sin9}{cos9-sin9} = tan54$

$\boxed{\rm Answer\:is\:option\:C}$

$\leadsto$ Concept of componendo - dividendo:-

If $\frac{a}{b} = \frac{x}{y}$,

then $\frac{(a+b)}{(a-b)} = \frac{(x+y)}{(x-y)}$

Answer 2

Answer:

Photosynthesis, the process by which green plants and certain other organisms transform light energy into chemical energy. During photosynthesis in green plants, light energy is captured and used to convert water, carbon dioxide, and minerals into oxygen and energy-rich organic compounds.

Step-by-step explanation:

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