cos 45/sec 30+cosec 30
Answers
Answer:
Answer:
\begin{gathered}Value \: of \:\frac{cos45}{(sec30+cosec30)}\\=\frac{\sqrt{6}(\sqrt{3}-1)}{8}\end{gathered}
Valueof
(sec30+cosec30)
cos45
=
8
6
(
3
−1)
Step-by-step explanation:
Value \: of \:\frac{cos45}{(sec30+cosec30)}Valueof
(sec30+cosec30)
cos45
=\frac{\frac{1}{\sqrt{2}}}{\frac{2}{\sqrt{3}}+2}=
3
2
+2
2
1
=\frac{\frac{1}{\sqrt{2}}}{\frac{2+2\sqrt{3}}{\sqrt{3}}}=
3
2+2
3
2
1
=\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2(1+\sqrt{3})}=
2
1
×
2(1+
3
)
3
=\frac{\sqrt{2}}{\sqrt{2}\times \sqrt{2}} \times \frac{\sqrt{3}\times (\sqrt{3}-1)}{2(\sqrt{3}+1)(\sqrt{3}-1)}=
2
×
2
2
×
2(
3
+1)(
3
−1)
3
×(
3
−1)
=\frac{\sqrt{6}(\sqrt{3}-1)}{4(\big(\sqrt{3}\big)^{2}-1^{2})}=
4((
3
)
2
−1
2
)
6
(
3
−1)
=\frac{\sqrt{6}(\sqrt{3}-1)}{4(3-1)}=
4(3−1)
6
(
3
−1)
=\frac{\sqrt{6}(\sqrt{3}-1)}{8}=
8
6
(
3
−1)
Therefore,
\begin{gathered}Value \: of \:\frac{cos45}{(sec30+cosec30)}\\=\frac{\sqrt{6}(\sqrt{3}-1)}{8}\end{gathered}
Valueof
(sec30+cosec30)
cos45
=
8
6
(
3
−1)
•••♪
Answer:
5/2√6
Explanation:
1/√2/√3/2+1/2=5/2√6