7.
If sin A -cos A = 7/13

Then is the value of sin A +cos A, where A is an acute angle is
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Answer:

17/13

Step-by-step explanation:

We know that sin²A + cos²A = 1

Now, sin A – cos A = 7/13

⇒ (sin A – cos A)² = (7/13)²

⇒ sin²A + cos²A – 2sinAcosA = 49/169

⇒ 1 – 2sinAcosA = 49/169

⇒ 2sinAcosA = 1 – 49/169 = (169 – 49)/169 = 120/169

⇒ 2sinAcosA = 120/169

⇒ 1 + 2sinAcosA = 1 + 120/169

⇒ sin²A + cos²A + 2sinAcosA = (169 + 120)/169

⇒ (sin A + cos A)² = 289/169

⇒ sin A + cos A = √(289/169)

⇒ sin A + cos A = 17/13

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