The way or form in which language is written known as:
Answers
Answer:
Question:
If tan θ = ¹/√7 then , show that \sf \dfrac{csc^2\theta-sec^2\theta}{csc^2\theta+sec^2\theta}=\dfrac{3}{4}
csc
2
θ+sec
2
θ
csc
2
θ−sec
2
θ
=
4
3
\huge\bold{Solution :}Solution:
★══════════════════════★
\sf tan\ \theta=\dfrac{1}{\sqrt{7}}tan θ=
7
1
:\to \sf tan^2\theta=\dfrac{1}{(\sqrt{7})^2}:→tan
2
θ=
(
7
)
2
1
:\to \sf \textsf{\textbf{\pink{tan$^\text{2} \boldsymbol \theta\ $ =\ $\dfrac{\text{1}}{\text{7}}$}}}\ \; \bigstar:→tan
2
θ =
7
1
★
\sf \dfrac{1}{cot\ \theta}=\dfrac{1}{\sqrt{7}}
cot θ
1
=
7
1
:\to \sf cot\ \theta=\sqrt{7}:→cot θ=
7
:\to \sf cot^2\theta=(\sqrt{7})^2:→cot
2
θ=(
7
)
2
:\to \sf \textsf{\textbf{\green{cot$^\text{2}\ \boldsymbol \theta $\ =\ 7}}}\ \; \bigstar:→cot
2
θ = 7 ★
★══════════════════════★
LHS
:\to \bf \blue{\dfrac{csc^2\theta-sec^2\theta}{csc^2\theta+sec^2\theta}}:→
csc
2
θ+sec
2
θ
csc
2
θ−sec
2
θ
From Trigonometric identities ,
csc²θ = 1 + cot²θ
sec²θ = 1 + tan²θ
:\to \sf \dfrac{(1+cot^2\theta)-(1+tan^2\theta)}{(1+cot^2\theta)+(1+tan^2\theta)}:→
(1+cot
2
θ)+(1+tan
2
θ)
(1+cot
2
θ)−(1+tan
2
θ)
tan²θ = ¹/₇
cot²θ = 7
:\to \sf \dfrac{(1+7)-(1+\frac{1}{7})}{(1+7)+(1+\frac{1}{7})}:→
(1+7)+(1+
7
1
)
(1+7)−(1+
7
1
)
:\to\ \sf \dfrac{8-\frac{8}{7}}{8+\frac{8}{7}}:→
8+
7
8
8−
7
8
:\to\ \sf \dfrac{48}{64}:→
64
48
:\to\ \textsf{\textbf{\orange{$\dfrac{\text{3}}{\text{4}}$}}}\ \; \bigstar:→
4
3
★
Answer:
written language is the representation of a spoken or gestural language by means of a writing system. Written language is an invention in that it must be taught to children, who will pick up spoken language or sign language by exposure even if they are not formally instructed.