solve this question please... no wrong answers.
Answers
Answer:
SOLUTION:
Let us assume that sin^-1(3/5) = x and sin^-1(8/17) = y.
\begin{gathered}\implies \bf \: \sin ^{ - 1} \bigg( \frac{3}{5} \bigg ) = x \\ \\ \implies \bf \: \sin \: x = \bigg( \frac{3}{5} \bigg ) \\ \\ \implies \bf \: \cos \: x \: = \sqrt{1 - \sin ^{2} x} \\ \\ \implies \: \bf \: \sqrt{1 - \bigg( \frac{3}{5} \bigg) ^{2} } \\ \\ \implies \: \bf \: \sqrt{1 - \bigg( \frac{9}{5} \bigg )} \\ \\ \implies \bf \: \frac{4}{5} \\ \\ \implies \bf \: \cos \: x \: = \frac{4}{5}\end{gathered}
⟹sin
−1
(
5
3
)=x
⟹sinx=(
5
3
)
⟹cosx=
1−sin
2
x
⟹
1−(
5
3
)
2
⟹
1−(
5
9
)
⟹
5
4
⟹cosx=
5
4
now find the value of of sin y
\begin{gathered}\implies \bf \sin ^{ - 1} \bigg( \frac{8}{17} \bigg) \: = y \\ \\ \implies \bf \sin \: y \: = \frac{8}{17} \\ \\ \implies \bf \sin \: y = \sqrt{1 - \sin^{2} y} \\ \\ \implies \: \bf \sqrt{1 - \bigg( \frac{8}{17} \bigg)^{2} } \\ \\ \implies \: \bf \: \sqrt{1 - \bigg( \frac{64}{289} \bigg) } \\ \\ \implies \: \bf \: \frac{15}{7} \\ \\ \implies \bf \: \sin \: y = \frac{15}{7}\end{gathered}
⟹sin
−1
(
17
8
)=y
⟹siny=
17
8
⟹siny=
1−sin
2
y
⟹
1−(
17
8
)
2
⟹
1−(
289
64
)
⟹
7
15
⟹siny=
7
15
As we know that cos(a-b) = cos a cos b + sin a sin b.
\begin{gathered}\implies \bf \: \cos(x - y) = \: \frac{4}{5} \times \frac{15}{7} + \frac{3}{5} \times \frac{8}{17} \\ \\ \implies \bf \: \cos(x - y) = \frac{60 + 24}{17 \times 5} \\ \\ \implies \bf \cos(x - y) = \frac{84}{85} \\ \\ \implies \bf \: (x - y) \ = cos ^{ - 1} \bigg(\frac{84}{85} \bigg)\end{gathered}
⟹cos(x−y)=
5
4
×
7
15
+
5
3
×
17
8
⟹cos(x−y)=
17×5
60+24
⟹cos(x−y)=
85
84
⟹(x−y) =cos
−1
(
85
84
)
Putting the value of x and y we get,
\implies \bf \sin ^{ - 1} \frac{3}{5} - \sin ^{ - 1} \frac{8}{7} = \cos ^{ - 1} \frac{84}{85}⟹sin
−1
5
3
−sin
−1
7
8
=cos
−1
85
84
LHS = RHS
HENCE PROVED
Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's metabolic activities.The process of photosynthesis is commonly written as: 6CO2 + 6H2O → C6H12O6 + 6O2. This means that the reactants, six carbon dioxide molecules and six water molecules, are converted by light energy captured by chlorophyll (implied by the arrow) into a sugar molecule and six oxygen molecules, the products.