Question

If cos^100x =1+sin^100x ,then the general value of x is​

Answer 1

Answer:

Now, maximum value of sin100x can be 1. So, above equation will satisfy only when cos100x=0. ∴sin100x=1andcos100x=0 is the only solution for this equation. ∴x=nπ+π2 is the general solution.

Answer 2

The General Solution is x=nπ+π/2

GIVEN: Cos¹⁰⁰ = 1 + Sin¹⁰⁰
TO FIND: General Solution of x.
SOLUTION:
​As we are given,

Cos¹⁰⁰ = 1 + Sin¹⁰⁰

Cos¹⁰⁰ - Sin¹⁰⁰ = 1

As we know,

−1 ≤ Sinx ≤ 1

Implying that,

0 ≤ sin¹⁰⁰ ≤ 1

Therefore, the Maximum Value of Sinx = 1

Similarly,

−1 ≤ Cosx ≤ 1

0 ≤ Cos¹⁰⁰ ≤ 1

Therefore, the Minimum Value of Cosx is 1

Now,

Sinx = 1                                       [found above]

Sin¹⁰⁰x = (Sin²x)⁵⁰                       [using identity]

(±1)² = 1

= sinπ/2

Therefore, The general solution for Cos¹⁰⁰ = 1 + Sin¹⁰⁰ is  sinπ/2.

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