find 3/4 of 124 and 840
Answers
Step-by-step explanation:
Hey there !!
→ Prove that :-)
\bf{ \frac{tan A}{(1 - cot A)} + \frac{cot A}{(1 - tan A)} = ( 1 + tan A + cot A ) .}
(1−cotA)
tanA
+
(1−tanA)
cotA
=(1+tanA+cotA).
→ Solution :-)
Given,,
\begin{lgathered}\begin{lgathered}\frac{\tan\theta}{1-\cot\theta}\;+\;\frac{\cot\theta}{1-\tan\theta}\\ \\=\frac{\tan\theta}{1-\cot\theta}\;+\;\frac{\cot\theta}{1-\frac{1}{\cot\theta}}\\ \\=\frac{\tan\theta}{1-\cot\theta}+\frac{\cot^{2}\theta}{\cot\theta-1}\\ \\=\frac{\tan\theta}{1-\cot\theta}-\frac{\cot^{2}\theta}{1-\cot\theta}\\ \\=\frac{\tan\theta-\cot^{2}\theta}{1-\cot\theta}\\ \\ =\frac{\frac{1}{\cot\theta}-\cot^{2}\theta}{1-\cot\theta}\\ \\=\frac{1-cot^{3}\theta}{\cot\theta(1-\cot\theta)}\\ \\=\frac{(1-cot\theta)(1+cot^{2}\theta+\cot\theta)}{\cot\theta(1-\cot\theta)}\\ \\=\frac{1+cot^{2}\theta+\cot\theta}{\cot\theta}\\ \\=\frac{1}{\cot\theta}+\frac{\cot^{2}\theta}{\cot\theta}+\frac{\cot\theta}{\cot\theta}\\ \\=\tan\theta+\cot\theta+1\;\;\;\textbf{Proved.}\end{lgathered}\end{lgathered}
1−cotθ
tanθ
+
1−tanθ
cotθ
=
1−cotθ
tanθ
+
1−
cotθ
1
cotθ
=
1−cotθ
tanθ
+
cotθ−1
cot
2
θ
=
1−cotθ
tanθ
−
1−cotθ
cot
2
θ
=
1−cotθ
tanθ−cot
2
θ
=
1−cotθ
cotθ
1
−cot
2
θ
=
cotθ(1−cotθ)
1−cot
3
θ
=
cotθ(1−cotθ)
(1−cotθ)(1+cot
2
θ+cotθ)
=
cotθ
1+cot
2
θ+cotθ
=
cotθ
1
+
cotθ
cot
2
θ
+
cotθ
cotθ
=tanθ+cotθ+1Proved.
Answer:
93 ,630.
Step-by-step explanation:
find 3/4 of 124 and 840
3/4 of 124
=3/4 ×124
= 93
3/4 of 840
=3/4 ×840
=630