Question

2log(sin a)+log(1+cot²a)=?​

Answer 1

Answer:

8There are five types of blood vessels: the arteries, which carry the blood away from the heart; the arterioles; the capillaries, where the exchange of water and chemicals between the blood and the tissues occurs; the venules; and the veins, which carry blood from the capillaries back towards the heart.

Answer 2

${\boxed{\boxed{\bf{Given \: Question :- }}}}$

$\bf \:Evaluate \: : 2log(sin a)+log(1+cot²a)$

$\huge \orange{AηsωeR} ✍$

${\boxed{\boxed{\bf{Formula \: used :-}}}}$

$\bf \:loga + logb = logab$

$\bf \:loga - logb = log\dfrac{a}{b}$

$\bf \:log {a}^{b} = b \: loga$

$\bf \: log(1) = 0$

$\begin{gathered}\Large{\bold{\red{\underline{CaLcUlAtIoN\::}}}} \end{gathered}$

$\bf \:Consider \: 2log(sin a)+log(1+cot²a)$

$\bf\implies \:2log(sin a)+log(cosec²a)$

$\bf\implies \:2log(sin a)+2log(coseca)$

$\bf\implies \:2(log(sin a)+log(coseca))$

$\bf\implies \:2log(sin a \times coseca)$

$\bf\implies \:2log(sin a \times \dfrac{1}{sin a} )$

$\bf\implies \:2 log(1) = 0$

$\large{\boxed{\boxed{\bf{Hence, 2log(sin a)+log(1+cot²a)=0}}}}$

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$\begin{gathered}\Large{\bold{\pink{\underline{More InFoRmAtIoN\::}}}} \end{gathered}$

Relationship between sides and T ratios

sin θ = Opposite Side/Hypotenuse

cos θ = Adjacent Side/Hypotenuse

tan θ = Opposite Side/Adjacent Side

sec θ = Hypotenuse/Adjacent Side

cosec θ = Hypotenuse/Opposite Side

cot θ = Adjacent Side/Opposite Side

Reciprocal Identities

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

sin θ = 1/cosec θ

cos θ = 1/sec θ

tan θ = 1/cot θ

Co-function Identities

sin (90°−x) = cos x

cos (90°−x) = sin x

tan (90°−x) = cot x

cot (90°−x) = tan x

sec (90°−x) = cosec x

cosec (90°−x) = sec x

Fundamental Trigonometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

cosec²θ - cot²θ = 1