Mathematics Test 74

Result

Mathematics Test 74

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Weekly Quiz Competition

Question 1
4 / -1

If cosx + secx = –2, then for a +ve integer n, cosⁿ x + secⁿ x is :-

A
always 2

B
always –2

C
–2 if n is odd and 2 if n is eve

D
–2 if n is even and 2 if n is odd

Solution

cos x + sec x = – 2

cos x + 1/cos x = – 2

cos²x + 2 cos x + 1 = 0

(cos x + 1)² = 0

cos x = – 1, sec x = – 1

cosⁿx + secⁿx

= (– 1)ⁿ + (– 1)ⁿ = 2 if n → even

– 2 if n → odd
Question 2
4 / -1

In ΔABC sin²A + sin²B + sin²C = 2 then triangle is :-

A
Equilateral

B
Right angle

C
Isoscelles

D
None

Solution

sin²A + sin²B + sin²C = 2

If A + B + C = π

then sin²A + sin²B + sin²C

2 + 2 cos A cos B cos C = 2

cos A cos B cos C = 0

A = π/2 or B = π/2 or C = π/2

Δ is right angle.