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प्रश्न
Evaluate the following without using a table:
`(sin 35° cos 55° + cos 35° sin 55°)/("cosec" 10° cos 80°)`
बेरीज
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उत्तर
Given:
`(sin 35° cos 55° + cos 35° sin 55°)/("cosec" 10° cos 80°)`
Step 1: Simplify
sinA cosB + cosA sinB = sin(A + B)
A = 35∘
B = 55∘
sin 35° cos 55° + cos 35° sin 55°
= sin(35° + 55°)
= sin 90° ⇒ 1 ...(i)
Step 2:
cosec 10° = `1/(sin 10°)`
cos 80° = sin 10° ...[since cos θ = sin(90 − θ)]
= cosec 10° ⋅ cos 80°
= `1/(sin 10°) ⋅ sin 10° = 1` ...(ii)
= `1/1` ...[Dividing (i) & (ii)]
= 1
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