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Question : 39 of 120
Marks:
+1 ,
-0
Solution:
Concept: Trigonometry Formula
cot ‌ θ = ‌ tan ‌ θ = ‌ c o s e c θ = ‌ sec ‌ θ = ‌ sin 2 θ + cos 2 θ = 1 ( sin ‌ θ + cos ‌ θ ) 2 = sin 2 θ + cos 2 θ + 2 ‌ sin ‌ θ ‌ cos ‌ θ Calculation: To Find: Value of
( 1 + cot ‌ θ − c o s e c θ ) ( 1 + tan ‌ θ + sec ‌ θ ) ‌ ‌ = ( 1 + ‌ − ‌ ) ( 1 + ‌ + ‌ ) ‌ ‌ = ‌ ( sin ‌ θ + cos ‌ θ − 1 ) ( sin ‌ θ + cos ‌ θ + 1 ) sin ‌ θ ‌ cos ‌ θ
‌ ‌ = ‌ ( sin ‌ θ + cos ‌ θ ) 2 − 1 sin ‌ θ ‌ cos ‌ θ
‌ ‌ = ‌ sin 2 θ + cos 2 θ + 2 ‌ sin ‌ θ ‌ cos ‌ θ − 1 sin ‌ θ ‌ cos ‌ θ
‌ ‌ = ‌ 1 + 2 ‌ sin ‌ θ ‌ cos ‌ θ − 1 sin ‌ θ ‌ cos ‌ θ
‌ ‌ = ‌ 2 ‌ sin ‌ θ ‌ cos ‌ θ sin ‌ θ ‌ cos ‌ θ
‌ ‌ = 2
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