# If Sec2a = Cosec(A - 42°), Where 2a is an Acute Angle, Then Find the Value of A. - Mathematics

Sum

If sec2A = cosec(A - 42°), where 2A is an acute angle, then find the value of A.

#### Solution

$\sec2A = cosec\left( A - 42^\circ \right)$

$\Rightarrow cosec\left( 90^\circ- 2A \right) = cosec\left( A - 42^\circ \right)$

Comparing both sides, we get

$90^\circ- 2A = A - 42^\circ$

$\Rightarrow 2A + A = 90^\circ + 42^\circ$

$\Rightarrow 3A = 132^\circ$

$\Rightarrow A = \frac{132^\circ}{3}$

$\therefore A = 44^\circ$

Hence, the value of A is 44°

Concept: Trigonometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 7 Trigonometric Ratios of Complementary Angles
Exercises | Q 11 | Page 314

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