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CBSE Class 12 Math 2020 Delhi Set 3 Solved Paper

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Question : 9 of 11
Marks: +1, -0
Section - C

Q. Nos. 27 to 32 carry 4 marks each.
Solve the equation x:sin‌−1(‌
5
x
)+sin‌−1(‌
12
x
)=‌
π
2
(x≠0)
Solution:  
sin‌−1‌
5
x
+sin‌−1‌
12
x
=‌
π
2

⇒‌
12
x
=sin‌(‌
π
2
−sin‌−1‌
5
x
)
⇒‌
12
x
=cos(sin‌−1‌
5
x
)
⇒‌
12
x
=√1−(‌
5
x
)2∵cos(sin‌−1x)=√1−x2
(‌
12
x
)2=1−‌
25
x2

⇒‌
144
x2
+‌
25
x2
=1
⇒‌
169
x2
=1
x2=169
⇒x=±√169
⇒x=13,−13
But x=−13 doesn't satisfy the given equation.
Hence the solution of the given equation is x=13.
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