Question

given sinx +cosx = 5/4. if 1 + 2sinxcosx = a then find the value of 32a =?

Answer 1

Hope u like my process
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Formula to be used :
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sin²x + cos²x =1

Given :: sinx + cosx =5/4
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1 +2sinxcosx = a

or, sin²x + cos²x + 2sinxcosx = a

or, (sinx + cosx)² = a

or, (5/4)² = a

Thus....

32a = 32× (5/4)² = 32 × 25/ 16

Thus, 32 a = 50

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Answer 2

Step-by-step explanation:

$\bf{question \: }$

given sinx+cosx=5/4. If 1+2sinxcosx=a,then find the value of 32a.

Solution:-

We have,

$\bf \: sinx+cosx= \frac{5}{4} \\ </p><p> \\ \bf \: If \: 1+2sinxcosx=a$

. Solving the equation:-

$\bf \: sinx+cosx= \frac{5}{4} \\ \\ \bf \:$

$\bf \: squaring \: both \: sides$

$\bf { sin }^{2} + {cos}^{2} =( { \frac{5}{4} })^{2}$

GIVEN:-

$\bf \: sin^2 x+cos ^2x+2 \: sinxcosx= \frac{25}{16} \:$

$\bf \: 1+2 \: sinxcosx= \frac{25}{16} \\ \: \bf \: a = \frac{25}{16}$

$\bf1 +2sinxcosx = a \\ </p><p></p><p> \bf \: or, \\ \bf\: sin^2x + cos^2x + 2sinxcosx = a \\ </p><p></p><p> \bf \: or, \\ \bf (sinx + cosx)^2= a</p><p> \:$

Then putting the value of a from task

$\bf32 \: a = 32 × \frac{25}{16} \\ \\ \bf 32 \: a = 2 \times 25 \\ \\ </p><p></p><p>\bf \red {32 \: a = 50}</p><p></p><p>\: </p><p>$